Aligner damage prediction and mitigation

ABSTRACT

Embodiments relate to an aligner breakage solution. A method includes obtaining a digital design of a polymeric aligner for a dental arch of a patient. The polymeric aligner is shaped to apply forces to teeth of the dental arch. The method also includes performing an analysis on the digital design of the polymeric aligner using at least one of a) a trained machine learning model, b) a numerical simulation, c) a geometry evaluator or d) a rules engine. The method may also include determining, based on the analysis, whether the digital design of the polymeric aligner includes probable points of damage, wherein for a probable point of damage there is a threshold probability that breakage, deformation, or warpage will occur. The method may also include, responsive to determining that the digital design of the polymeric aligner comprises probable points of damage, performing corrective actions based on the probable points of damage.

RELATED APPLICATIONS

This patent application claims the benefit under 35 U.S.C. § 119(e) ofU.S. Provisional Application No. 62/737,458, filed Sep. 27, 2018, whichis incorporated by reference herein.

TECHNICAL FIELD

The present disclosure relates to the field of designing dentalappliances, such as polymeric orthodontic aligners and, in particular,to designing physical properties of polymeric aligners in light ofdesired or acceptable manufacturing or clinical outcomes that may beachieved by those polymeric aligners, and to predicting failures of suchpolymeric aligners.

BACKGROUND

An objective of orthodontics is to move a patient's teeth to positionswhere function and/or aesthetics are optimized. Traditionally,appliances such as braces are applied to a patient's teeth by anorthodontist or dentist and the set of braces exerts continual force onthe teeth and gradually urges them toward their intended positions. Overtime and with a series of clinical visits and adjustments to the braces,the orthodontist adjusts the appliances to move the teeth toward theirfinal destination.

Alternatives to conventional orthodontic treatment with traditionalaffixed appliances (e.g., braces) include systems including a series ofpreformed aligners. In these systems, multiple, and sometimes all, ofthe aligners to be worn by a patient may be designed and/or fabricatedbefore the aligners are administered to a patient and/or reposition thepatient's teeth (e.g., at the outset of treatment). The design and/orplanning of a customized treatment for a patient may make use ofcomputer-based three-dimensional (3D) planning/design tools. The designof the aligners can rely on computer modeling of a series of plannedsuccessive tooth arrangements, and the individual aligners are designedto be worn over the teeth and elastically reposition the teeth to eachof the planned tooth arrangements.

Once designed and/or planned, a series of preformed aligners may befabricated from a material that, alone or in combination withattachments on a patient's teeth, imparts forces to the patient's teeth.Example materials include one or more polymeric materials. Fabricationmay involve thermoforming aligners using a series of molds (e.g.,3D-printed molds) and/or directly fabricating the aligners. For somethermoforming fabrication techniques, shells are formed around molds toachieve negatives of the molds. The shells are then removed from themolds to be used for various applications. One example application inwhich a shell is formed around a mold and then later used is correctivedentistry or orthodontic treatment. In such an application, the mold maybe a positive mold of a dental arch for a patient and the shell may bean aligner to be used for aligning one or more teeth of the patient.When attachments (e.g., planned orthodontic attachments) are used, themold may also include features associated with the attachments.

Molds may be formed using a variety of techniques, such as with castingor rapid prototyping equipment. For example, 3D printers may manufacturemolds of aligners using additive manufacturing techniques (e.g.,stereolithography) or subtractive manufacturing techniques (e.g.,milling).The aligners may then be formed over the molds usingthermoforming techniques. Once an aligner is formed, it may be manuallyor automatically trimmed. In some instances, a computer controlled4-axis or 5-axis trimming machine (e.g., a laser trimming machine or amill) is used to trim the aligner along a cutline. The trimming machineuses electronic data that identifies the cutline to trim the aligner.Thereafter, the aligner may be removed from the mold and delivered tothe patient. As another example, aligners may be directly fabricatedusing, e.g., stereolithography (SLA), digital light processing (DLP),and/or other 3D printing techniques.

While it may be desirable to identify specific portions of alignersprone to deformation, warpage and/or breakage during fabrication (e.g.,in response to removal from a mold) and/or use (e.g., in response toremoval from a patient's dentition), existing techniques make itdifficult to do so.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure is illustrated by way of example, and not by wayof limitation, in the figures of the accompanying drawings.

FIG. 1A illustrates a flow diagram for a method of performing acorrective analysis on a digital design of a polymeric aligner, inaccordance with one embodiment.

FIG. 1B illustrates a flow diagram of selecting a manufacturing flow forone or more aligners based on damage predictions for the one or morealigners, in accordance with one embodiment.

FIG. 2A illustrates a method of training a machine learning model topredict whether an orthodontic aligner will be damaged duringmanufacture of the orthodontic aligner, in accordance with oneembodiment.

FIG. 2B illustrates a flow diagram for a method of performing analysison a digital design of an orthodontic aligner using a trained machinelearning model, in accordance with one embodiment.

FIG. 2C illustrates a flow diagram for a method of determining whetheran orthodontic aligner will become damaged (e.g., break) during or aftermanufacturing of the orthodontic aligner using a trained machinelearning model, in accordance with one embodiment.

FIG. 2D illustrates a flow diagram for a method of determining whetherany orthodontic aligner in a set of orthodontic aligners associated witha treatment plan for a patient will become damaged (e.g., break) using atrained machine learning model, in accordance with one embodiment.

FIG. 3A illustrates a flow diagram for a method of performing analysison a digital design of a polymeric aligner using numerical simulation,in accordance with one embodiment.

FIG. 3B illustrates an example numerical simulation associated withremoval of a digital design of a polymeric aligner from a dentalarch-like structure, in accordance with one embodiment.

FIG. 4A illustrates a flow diagram for a method of performing analysison a digital design of a polymeric aligner using numerical simulation bymodeling teeth and bonded attachments of a dental arch as springs, inaccordance with one embodiment.

FIG. 4B illustrates an example numerical simulation that models teeth ofthe dental arch of the patient as springs, in accordance with oneembodiment, in accordance with one embodiment.

FIG. 5A illustrates a flow diagram for a method of performing analysison a digital design of a polymeric aligner using numerical simulation bymodeling a subset of teeth and bonded attachments of a dental arch assprings, in accordance with one embodiment.

FIG. 5B illustrates an example numerical simulation that models a subsetof teeth of the dental arch of the patient as springs, in accordancewith one embodiment, in accordance with one embodiment.

FIG. 6A illustrates a flow diagram for a method of performing analysison a digital design of an aligner (e.g., a polymeric aligner) usingnumerical simulation, in accordance with one embodiment.

FIG. 6B illustrates application of a bending load around a region of analigner, in accordance with one embodiment.

FIG. 6C illustrates application of a twisting load around a region of analigner, in accordance with one embodiment.

FIG. 6D illustrates application of a uniaxis tension load around aregion of an aligner, in accordance with one embodiment.

FIG. 6E illustrates application of a shear load around a region of analigner, in accordance with one embodiment.

FIG. 6F illustrates weak spots of an aligner, in accordance with oneembodiment.

FIG. 7A illustrates a flow diagram for a method of performing analysison a digital design of an aligner (e.g., a polymeric aligner) using ageometrical evaluator, in accordance with one embodiment.

FIG. 7B illustrates an aligner including teeth-receiving cavities andinterproximal regions between pairs of teeth-receiving cavities, inaccordance with one embodiment.

FIG. 7C illustrates a cross-sectional slice taken of an aligner, inaccordance with one embodiment.

FIG. 7D illustrates a bending load applied around a first axis of thecross-sectional slice of FIG. 7C, in accordance with one embodiment.

FIG. 7E illustrates a bending load applied around a second axis of thecross-sectional slice of FIG. 7C, in accordance with one embodiment.

FIG. 7F illustrates a torsion load applied around a third axis normal tothe cross-sectional slice of FIG. 7C, in accordance with one embodiment.

FIG. 7G illustrates an overlay of three different aligners for a dentalarch, wherein each of the aligners is associated with a different stageof treatment of the dental arch, in accordance with one embodiment.

FIG. 8A illustrates a flow diagram for a method 800 of performinganalysis on a digital design of an aligner (e.g., a polymeric aligner)using numerical simulation that simulates a sequence of loads on thealigner, in accordance with one embodiment.

FIG. 8B illustrates a stress strain curve for an aligner, in accordancewith one embodiment. Stress (a) may represent force and strain (c) mayrepresent displacement.

FIG. 8C illustrates a flow diagram for a method of performing analysison a digital design of an aligner (e.g., a polymeric aligner) usingnumerical simulation associated with chewing and/or grinding of teeth,in accordance with one embodiment.

FIG. 9 illustrates a flow diagram for a method for implementing one ormore corrective actions to a polymeric aligner based on a simulatedremoval of the polymeric aligner from a dental arch.

FIG. 10 illustrates a flow diagram for a method of performing analysison a digital design of a polymeric aligner using a rules engine, inaccordance with one embodiment.

FIG. 11 illustrates a flow diagram for a method of outputting a filteredset of possible treatment plans, in accordance with one embodiment.

FIG. 12 illustrates a flow diagram for a method of performing numericalsimulation on digital designs of a polymeric aligner to generate rulesfor a rules engine, in accordance with one embodiment.

FIG. 13 illustrates a flow diagram for a method of using a rules engineon a digital design of a polymeric aligner to identify a probable pointof damage and then performing a numerical simulation of the digitaldesign of the polymeric aligner, in accordance with one embodiment.

FIG. 14 illustrates a block diagram of an example computing device, inaccordance with embodiments of the present disclosure.

FIG. 15A illustrates a tooth repositioning appliance, in accordance withembodiments.

FIG. 15B illustrates a tooth repositioning system, in accordance withembodiments.

FIG. 15C illustrates a method of orthodontic treatment using a pluralityof appliances, in accordance with embodiments.

FIG. 16 illustrates a method for designing an orthodontic appliance, inaccordance with embodiments.

FIG. 17 illustrates a method for digitally planning an orthodontictreatment, in accordance with embodiments.

FIG. 18 illustrates another method for implementing one or morecorrective actions to a polymeric aligner based on a simulated removalof the polymeric aligner from a dental arch.

DETAILED DESCRIPTION

Aligners (also referred to herein as “orthodontic aligners”) may be onetype of dental appliance (also referred to herein as “appliance”)applied to a patient's dentition and used to treat malocclusions.Examples of aligners and aligner systems may be found in FIGS. 15A and15B. An example treatment method using aligners is shown in FIG. 15C.Aligners may be formed from polymeric materials using indirect or directfabrication techniques, examples of which may be found in conjunctionwith the discussion of FIGS. 15A, 15B, and 15C. As noted further herein,during the indirect fabrication of aligners, many aligners mayexperience strains/stresses from being removed from molds. Additionally,during use (whether aligners are formed indirectly or directly), manyaligners may experience strains/stresses from residing in an intra-oralenvironment for extended periods of time (e.g., up to twenty-three hoursa day for several weeks) or from being repeatedly removed (e.g., up toseveral times a day for several weeks) from a patient's dentition. Thestrains/stresses may result in physical damage (deformation (permanentor otherwise), warpage, breakage, cracks, damage, etc.) of aligners.Physical damage during manufacturing processes may present seriousproblems, including materials waste issues, supply chain issues, andinability to meet consumer demands. Physical damage during use may alsopresent serious problems, such as adversely affecting staging scenariosand/or the efficacy of treatment plans.

The embodiments herein relate to systems, methods, and/orcomputer-readable media suitable for predicting deformation, warpage,and/or breakage of custom manufactured products (e.g., of aligners)prior to and/or during fabrication (e.g., in response to removal from amold) and/or use (e.g., in response to removal from a patient'sdentition). Also discussed are embodiments that cover resolving and/ormitigating predicted points of damage. The embodiments described hereinfurther cover techniques to optimize properties, such as thicknesses, ofaligners by predicting portions of aligners that are prone todeformation, warpage, breakage, etc., and by identifying the extentthese properties accord with desired and/or actual clinical goals.Various embodiments may further use optimized properties of aligners asthe basis of efficient aligner manufacturing processes, customizedand/or optimized treatment plans, etc. Alone and together, thesefeatures may be considered as one or more aligner damage solutions,e.g., solutions that accommodate possible physical damage to alignersthrough manufacturing, use, etc.

More specifically, in some embodiments, the aligner damage solutionsystems and methods may be implemented during the design of orthodonticaligners prior to and/or during manufacturing. Designing custommanufactured products can be particularly difficult, especially inorthodontic aligner manufacturing scenarios in which orthodonticaligners are individually customized for every single patient.Additionally, many orthodontic treatment plans prescribe treatment by aseries of aligners that are manufactured for a patient. Each aligner inthe series of aligners may implement a specific stage of a treatmentplan, and/or have unique properties (e.g., shape(s)) compared to otheraligners in the series of aligners. Additionally, many orthodontictreatment plans may provide patients with a pair of aligners for eachstage of treatment, one unique upper aligner for treating the upperdental arch and one unique lower aligner for treating the lower dentalarch. As a result, in some instances, a single treatment can include50-60 stages for treating a complex case, meaning 100-120 uniquealigners are designed to be manufactured for a single patient.

Further, for aligners manufactured by indirect fabrication techniques(e.g., thermoforming), removing an aligner from a mold may causeforce(s) and/or a moment(s) to be applied to the aligner. In someinstances, the polymeric materials of the aligners may break, warp,and/or deform during the removal process due to the force exerted.Further, removing aligners from a patient's teeth may cause force(s)and/or torque(s) to be exerted on the aligners, which may also break,warp, or deform the aligners. Patients may request a replacement alignerif the aligner breaks. As a result, another aligner is manufactured andshipped to the patient. As may be appreciated, as the number ofreplacement aligners increases, so too does the cost of manufacturing.In some instances, a replacement aligner may be manually modified postmanufacturing to attempt to account for possible breakage. For example,if a certain interproximal region is identified where the aligner broke,a filler material may be added to the aligner to strengthen the aligner.Manually modifying the aligners post manufacturing may be cumbersome andslow, especially if there are hundreds, thousands, or more replacementaligners requested. Further, modifying the replacement aligners is areactive process that is performed after the original aligner had anissue. Accordingly, embodiments of the present disclosure may provide amore scalable, automated, and/or proactive solution that may detectprobable points of damage in a design of an aligner and perform one ormore corrective actions prior to the aligner being manufactured.Embodiments may reduce the occurrence of aligner damage, and thus mayalso reduce the number of replacement aligners that are manufactured.Such reduction in damages may reduce the overall cost of manufacturingaligners and may reduce the amount of time that technicians spend onresolving aligner damages.

As noted herein, an aligner may be formed from a polymeric shell that isconfigured to receive an upper or lower dental arch of a patient at aparticular treatment stage. Each aligner may be configured to applyforces to the patient's teeth at the particular stage of the orthodontictreatment. The aligners each have teeth-receiving cavities that receiveand resiliently reposition the teeth in accordance with a particulartreatment stage. Each tooth-receiving cavity may be referred to as a“cap”. Teeth may be repositioned by the aligners by, for example, movingone or more teeth vertically (e.g., extruding or intruding teeth),rotating one or more teeth (e.g., through moments applied to the teeth,through second/third order rotations, etc.), moving one or more teeth ina transverse direction relative to the dental arch, and/or moving one ormore teeth in an anterior-posterior direction relative to the dentalarch. Each aligner may additionally include shapes that accommodatefeatures attached to a patient's dentition that facilitate toothrepositioning and/or rotation.

Embodiments may identify individual aligners that include probablepoints of failure and/or may identify sets of aligners (e.g., for apatient or for a particular dental arch of a patient) that include onemore aligner with a probable point of failure. Manufacturing flows maybe determined for aligners based upon a likelihood that those alignerswill become damaged (e.g., will develop a point of damage).Manufacturing flows may also be determined for sets of aligners (e.g.,all aligners associated with a treatment plan for a patient, or allaligners associated with a treatment plan for an upper or lower dentalarch of the patient) based on the probability that any aligners in theset of aligner will become damaged or experience a failure.

As mentioned above, the embodiments may determine various probablepoints of damage for a given set of digital designs of aligners. One ormore probable points of damage may include one or more of breakage,warpage, deformation, failure, and so forth. Detecting the probablepoints of damage may enable modifying or fixing the digital design ofthe aligner to remove the probable points of damage prior tomanufacturing the aligner, thereby increasing the yield of aligners thatare successfully manufactured, reducing the number of patient complaintsrelated to the aligners failing, reducing manufacturing cost ofreplacement aligners, and/or preventing the manufacturing of an alignerincluding a probable point of damage. It is noted that “probable” pointsof damage (used interchangeably with “likely” points of failure), asused herein, may refer to a likeliness of damage to a given region of analigner by, e.g., manufacturing or use. Probable points of damage neednot indicate damage by, e.g., a preponderance. Probable points of damagemay indicate likeliness of damage beyond any specified threshold,including by a preponderance.

In some embodiments, the determination of the probable points of damagemay be made based on a digital design of the aligner. The digital designof the aligner may refer to a digital model of the aligner including ageometry of the aligner. In some embodiments, the digital model for eachaligner may be included in a digital file associated with the aligner.In some embodiments, the digital model of the aligner may be generatedbased on scanning the aligner (e.g., using an intraoral scanner or other3D scanner) and generating the digital model of the aligner from aresult of the scanning. In other embodiments, the digital model of thealigner may be generated using a digital model of a mold of the dentalarch of the patient. The digital model of the mold may be offset (e.g.,enlarged) to generate the digital model of the aligner. The “digitaldesign of the aligner” and the “digital model of the aligner” may beused interchangeably herein. An analysis may be performed on the digitaldesign of the aligner using at least one of a) a trained machinelearning model trained to identify aligners having probable points ofdamage, b) a numerical simulation associated with removal of the alignerfrom a mold of the dental arch of the patient, c) a numerical simulationassociated with progressive damage to the aligner, d) a numericalsimulation that simulates loading around weak spots (e.g., interproximalregions) in the aligner, e) a geometry evaluator that calculates andevaluates geometry-related parameters (e.g., cross-sectional parameters)of the aligner (e.g., that evaluates a parameters associated with ageometry of the aligner), or f) a rules engine including one or morerules associated with parameters of aligners indicative of points ofdamage. Based on the analysis, a determination may be made as to whetherthe digital design of the aligner includes one or more probable pointsof damage. For a probable point of damage to be present, there is atleast a threshold probability that breakage, deformation, warpage,failure, etc. will occur. In response to determining that the digitaldesign of the aligner includes the one or more probable points ofdamage, one or more corrective actions (e.g., modifying the digitaldesign of the aligner, modifying attachments in the digital design ofthe aligner, providing a notification to a dental practitioner, etc.)may be performed based on the one or more probable points of damage.Some advantages of the disclosed embodiments may include automateddetection of various probable points of damage in aligners, automatedcorrection of the probable points of damage in aligners, and/orautomated selection of a manufacturing flow for aligners based on theexistence or lack of probable points of failure/damage in the aligners.The embodiments may also reduce the number of replacement aligners thatare manufactured, thereby reducing manufacturing costs and improvingcustomer satisfaction. In some implementations, the determination ofprobable points of damage may form the basis of the design of alignershaving variable thicknesses to accommodate those points of damage. Suchvariable thicknesses to accommodate points of damage may be formedthrough direct fabrication techniques and/or other techniques. Further,the embodiments may improve the number of aligners that are manufacturedwithout breakages, warpages, or deformations.

Various software and/or hardware components may be used to implement thedisclosed embodiments as shown in FIG. 14. For example, softwarecomponents may include computer instructions stored in a tangible,non-transitory computer-readable media that are executed by one or moreprocessing devices to perform the aligner damage solution on digitaldesigns of aligners. Hardware components may include a processingdevice, memory device, network device, and so forth.

The shape of an aligner, including the shapes of each tooth receivingcavity (cap) in the aligner, the shapes of interproximal regions betweentooth receiving cavities, the shapes of the outlines, the shapes ofadditional cavities formed to accommodate attachments on a patient'steeth, and so on all affect whether a particular aligner will break,warp or become otherwise deformed or damaged during removal of thealigner from a dental arch-like structure (e.g., mold and/or a patient'sdentition). As noted herein, the shape of an aligner may be modified toaccommodate probable points of damage and may form the basis of analigner with variable thicknesses. An aligner with a modified shape maybe formed by various techniques, including but not limited to directfabrication techniques.

In the embodiments disclosed herein, the digital design of each alignerfor a treatment plan or each aligner in specific stages of the treatmentplan may be analyzed to determine whether one or more probable points ofdamage are present at any locations of the digital design of thealigner. Each digital design of an aligner may be associated with adigital design of a dental arch at a treatment stage for a patient. Ifone or more probable points of damage are detected for a digital designof an aligner, corrective actions may be performed based on the probablepoints of damage.

Embodiments are described with reference to aligners and orthodonticaligners (e.g., polymeric aligners and polymeric orthodontic aligners).Aligners are one form of dental appliance (also referred to simply as anappliance for convenience). In particular, as described above and ingreater detail below, aligners may be a type of polymeric shell used tocorrect, for example, malocclusions. It should be understood that theembodiments described herein with reference to aligners also apply toother types of dental appliances and shells, and in particular to othertypes of polymeric dental appliances, including but not limited to sleepapnea treatment devices, night guards, and so on.

Once designed, each aligner may be manufactured by forming polymericmaterial to implement one or more stages of a treatment plan on apatient's dentition, e.g., through indirect fabrication techniques ordirect fabrication techniques. Examples of indirect and directfabrication techniques are further described herein with respect toFIGS. 15A, 15B, and 15C. For example, FIG. 1A illustrates a flow diagramfor a method 100 of performing a corrective analysis on a digital designof a polymeric aligner, in accordance with one embodiment. One or moreoperations of method 100 are performed by processing logic of acomputing device. The processing logic may include hardware (e.g.,circuitry, dedicated logic, programmable logic, microcode, etc.),software (e.g., instructions executed by a processing device), firmware,or a combination thereof. For example, one or more operations of method100 may be performed by a processing device executing an aligner designanalysis module 1450 of FIG. 14. It should be noted that the method 100may be performed for each unique aligner for each patient's treatmentplan, or for each unique aligner at one or more stages (e.g., keystages) of the treatment plan.

At block 102, processing logic may obtain a digital design of an alignerfor a dental arch of a patient. The aligner (e.g., a polymeric aligner)in the digital design is shaped to apply forces to one or more teeth ofthe dental arch. In some embodiments, the processing logic may receive afile including the digital model of the mold used to create theparticular aligner. The processing logic may manipulate (e.g., enlarge)the geometry of the digital model of the mold to dynamically generatethe digital design of the aligner. In some embodiments, the processinglogic may receive the digital design of the aligner from another systemor by scanning a manufactured aligner. In some embodiments, the digitaldesign of the aligner is a virtual three-dimensional (3D) model of thealigner that was generated based on a virtual 3D model of the dentalarch at a treatment stage.

At block 104, processing logic may perform an analysis on the digitaldesign of the polymeric aligner using at least one of a) a trainedmachine learning model trained to identify polymeric aligners havingprobable points of damage, b) a numerical simulation associated withremoval of the polymeric aligner from a mold of the dental arch of thepatient, c) a numerical simulation associated with progressive damage tothe aligner, d) a numerical simulation that simulates loading aroundweak spots (e.g., interproximal regions) in the aligner, e) a geometryevaluator that evaluates a parameters associated with a geometry of thepolymeric aligner, or f) a rules engine comprising one or more rulesassociated with parameters of polymeric aligners indicative of points ofdamage. Additional details related to performing the analysis on thedigital design of the polymeric aligner using the trained machinelearning model are discussed below with reference to FIGS. 2A-2D.Additional details related to performing the analysis on the digitaldesign of the aligner using the numerical simulation associated withremoval of the aligner from the mold are discussed below with referenceto FIGS. 3A-5B. Additional details related to performing the analysis ofthe digital design of the aligner using the numerical simulationassociated with progressive damage to the aligner are discussed withreference to FIGS. 8A-8C Additional details related to performing theanalysis of the digital design of the aligner using the numericalsimulation and/or a geometrical evaluator that simulates loading aroundweak spots of the aligner are discussed with reference to FIGS. 6A-7G.Additional details related to performing the analysis on the digitaldesign of the aligner using the rules engine are discussed below withreference to FIG. 10.

At block 106, processing logic may determine, based on the analysis,whether the digital design of the aligner includes one or more probablepoints of damage. A probable point of damage may refer to a point havingat least a threshold probability that breakage, deformation, or warpagewill occur as a result of removing the aligner from the mold, removingthe aligner from teeth, use of the aligner, and so forth. At block 107,processing logic determines whether any probable points of damage wereidentified. If at least one probable point of damage was identified, themethod continues to block 108. Otherwise the method may end.

At block 108, processing logic may perform one or more correctiveactions and/or select a manufacturing flow based on the one or moreprobable points of damage. In some embodiments, performing the one ormore corrective actions includes modifying the digital design of thealigner to generate a modified digital design of the aligner. In someembodiments, performing the one or more corrective actions includesmodifying a digital design of a dental arch associated with a digitaldesign of the aligner. Due to the change in the digital design of thedental arch, the digital design of the aligner may also be changed toaccommodate the change in the digital design of the dental arch.

If a probable point of damage is determined to be at or near a outlineof the digital design of the aligner, modifying the digital design ofthe aligner may include modifying the outline radius of the digitaldesign of the aligner. For example, the outline may be lowered to bemore straight, as opposed to more pointed (weakens the strength of thealigner at that point), in the digital design of the aligner.Straightening the outline may increase the strength of the aligner atthat location and may remove the probable point of damage from thedigital design of the aligner. If a probable point of damage isdetermined to be at or near an interproximal region between two teeth,modifying the digital design of the aligner may include modifying athickness of a portion of the digital design of the aligner. Forexample, increasing the thickness of the portion of the digital designof the aligner makes an outer surface of the digital design of thealigner flatter. Thickening the portion of the digital design maystrengthen the aligner at the portion and may remove the probable pointof damage in the digital design of the aligner. In some embodiments, thethickness of the aligner is controllable for aligners that are directlymanufactured using 3D printing techniques but is not controllable foraligners that are manufactured by a thermoforming process.

In some embodiments, modifying the digital design of the aligner mayinclude inserting an indicator in the digital design of the aligner. Theindicator represents a recommended place to begin removing the aligner.A location for placing the indicator may be determined during theanalysis performed on the digital design. For example, the analysis mayidentify that applying force at a certain location on the digital designof the aligner to remove the digital design of the aligner is lesslikely to cause damage than any other location on the digital design ofthe aligner. Accordingly, the indicator may be placed at that certainlocation.

In some embodiments, if a probable point of damage is determined to bepresent at or near a location in the digital design of the aligner thatis associated with an attachment (to a tooth, then performing thecorrective action may include modifying one or more attachmentsassociated with the probable point of damage on one or more teeth in thevirtual 3D model of the dental arch. Modifying the 3D model of thedental arch may cause a modified virtual 3D model of the aligner to begenerated based on the changes to the attachments. For example, a cavityof the aligner that accommodates the attachment may be moved, increasedor decreased in size, or have a shape changed in the modified virtual 3Dmodel of the aligner based on the change to the attachment in the 3Dmodel of the dental arch.

In some embodiments, if a probable point of damage is determined to bepresent at or near a location between two teeth, then performing thecorrective action may include adding a new virtual filler or enlargingan existing virtual filler to one or more locations on the virtual 3Dmodel of the dental arch associated with the one or more probable pointsof damage. A virtual filler may refer to a digital feature of or addedto a virtual model (such as a virtual model of a dental arch) thatpresents an additional object between two or more adjacent teeth. Inembodiments, the virtual filler of the virtual model changes thegeometry of a respective physical mold and reduces the probability offabrication issues. A modified virtual 3D model of the aligner may begenerated based on the modified virtual 3D model of the dental archincluding the virtual fillers. The virtual fillers may cause the alignerto have a flatter surface between the two teeth to accommodate thevirtual filler. A flatter surface between the teeth may increase thestrength of the aligner and remove the probable point of damage from thedigital design of the aligner.

After any of the modifications are made to the digital design of thealigner, a modified virtual 3D model of the aligner may be generatedbased on the modifications to the digital design of the aligner.Processing logic may determine whether the modified digital design ofthe aligner includes the one or more probable points of damage.Responsive to determining that the modified digital design of thealigner includes one or more probable points of damage, processing logicmay perform one or more second corrective actions based on the probablepoints of damage. This process may be repeated until all of the probablepoints of damage are removed from the digital design of the aligner,only a threshold number of probable points of damage are still presentin the digital design of the aligner, or the like.

In some embodiments, the digital design of the aligner is receivedduring a treatment planning phase of orthodontic treatment. When one ormore probable points of damage are determined to be present in thedigital design of the aligner, in some embodiments, the correctiveaction may include recommending modification of one or more attachmentson one or more teeth of the patient to reduce a probability that theprobable point will fail to below the threshold probability. In someembodiments, the corrective action may include recommending modificationof the digital design of the aligner to move one or more teeth usinganother digital design of another aligner in a different stage of atreatment plan for the patient to reduce the probability that theprobable point will fail below the threshold probability. For example, aparticular tooth rotation may be specified in a first stage of atreatment plan, and that particular tooth rotation may be achieved usinga particular attachment. The treatment plan may be modified to move theparticular tooth rotation to a later stage in treatment, thereby causingthe use of the particular attachment to also be moved to the later stagein treatment.

In some embodiments, the corrective action may include recommending oneor more processes to properly remove the aligner from the dental arch ofthe patient to reduce the probability that the probable point will failbelow the threshold probability. In some embodiments, the correctiveaction may include notifying a dental practitioner during the treatmentplanning phase that the digital design of the aligner has a probablepoint of damage. For example, if the probable point of damage cannot beremoved by modifying the digital design of the aligner, then processinglogic may notify the dental practitioner of the probable point ofdamage.

In some embodiments, performing the corrective action based on the oneor more probable points of damage may include setting a flag associatedwith the aligner to indicate that quality inspection should be performedon the aligner after manufacturing. The flag may cause the qualityinspection to target the one or more probable points of damage. In someembodiments, the corrective action may include recommending thattargeted inspection be performed by sending a notification to a systemof an inspector.

In some embodiments, performing the corrective action based on the oneor more probable points of damage may include setting a flag to use abreakable mold or mold with weakened regions during manufacturing. Abreakable mold may refer to a mold that is broken to remove the alignerfrom the breakable mold. Less force may be applied to the aligner whilethe mold is broken, and thus, the probability that the aligner will failduring removal may be reduced.

In some embodiments, performing the corrective action based on the oneor more probable points of damage may include changing a geometry of thevirtual 3D model of the mold. For example, a portion of the virtual 3Dmodel of the mold may be bubbled out or thickened. A modified virtual 3Dmodel of the aligner may be generated based on the modified virtual 3Dmodel of the mold, and the shape of the modified virtual 3D model may bechanged from the original virtual 3D model of the aligner due to theportion of the modified 3D model of the mold. By bubbling out,thickening or expanding the digital model (and thus the aligner) at oneor more locations, the amount of force that is needed to remove thealigner from the mold (or dental arch) at that location is reduced.Thus, breakage, warpage, etc. at that location may be mitigated.

In some embodiments, a manufacturing flow may be selected for an alignerat block 108 based on a prediction of a probable point of damage orfailure for the aligner or based on a lack of a probable point of damageor failure for the aligner.

FIG. 1B illustrates a method 110 of selecting a manufacturing flow forone or more aligners. One or more operations of method 110 are performedby processing logic of a computing device. The processing logic mayinclude hardware (e.g., circuitry, dedicated logic, programmable logic,microcode, etc.), software (e.g., instructions executed by a processingdevice), firmware, or a combination thereof. For example, one or moreoperations of method 110 may be performed by a processing deviceexecuting an aligner design analysis module 1450 of FIG. 14. It shouldbe noted that the method 110 is described with reference to sets ofaligners, such as aligners that are part of a treatment plan for apatient, or aligners that are associated with a treatment plan for aparticular dental arch of the patient. However, in embodiments method110 may be performed for each unique aligner for each patient'streatment plan, or for each unique aligner at key stages of thetreatment plan. In embodiments, method 110 may be performed at block 108of method 100.

At block 112 of method 110, processing logic receives data on probablepoints of failure for a plurality of aligners. The data may be foraligners associated with one or more orthodontic treatment plans for oneor more patients. The data on the probability of points of failure mayhave been output by a) a trained machine learning model trained toidentify aligners having probable points of damage, b) a numericalsimulation associated with removal of the aligner from a mold of thedental arch of the patient, c) a numerical simulation associated withprogressive damage to the aligner, d) a numerical simulation thatsimulates loading around weak spots in the aligner, e) a geometryevaluator that evaluates parameters associated with a geometry of thepolymeric aligner, or f) a rules engine comprising one or more rulesassociated with parameters of aligners indicative of points of damage.In some embodiments, data on the probability of points of failure mayhave been generated by two or more of the aforementioned simulators,rule engines and/or machine learning models.

At block 114, processing logic aggregates the data for the aligners thatis associated with the same treatment plan into one or more sets. In oneembodiment, the failure probability data for all aligners associatedwith a treatment plan is aggregated into a single set. Alternatively,the failure probability data for aligners associated with the sametreatment plan may be aggregated into two or more sets. For example, thedata associated with a lower dental arch of a patient (e.g., data foreach treatment stage of the lower dental arch) may be combined into afirst data set, and the data associated with an upper dental arch of thepatient may be combined into a second data set.

If probabilities of points of aligners being damaged are provided by twoor more different techniques (e.g., by a machine learning model and asimulation output, or by two simulation outputs, or by geometryevaluation), then the predictions of the multiple techniques may becombined to improve an accuracy of the prediction. For example, data maybe received for a single aligner, where that data includes a firstprobability of the aligner failing as output by a machine learning modeland further includes a second probability of the aligner failing asoutput by a numerical simulation.

At block 116, each of the one or more data sets is assessed to determinewhether all of the aligners in any of the data sets has a probability ofdamage/failure that is below a lower probability threshold. The lowerthreshold may have, for example, a value of a 2%, 5%, 10%, 15%, or 20%chance of a point of damage/failure. Aligner sets that have no alignerswith points having a probability of damage/failure that meets or exceedsthe lower threshold may be identified as particularly low risk alignersets. Such low risk aligner sets may be fast tracked with minimalmanufacturing steps, which may reduce a cost of manufacturing suchaligner sets and speed up the manufacture process for such aligner sets.Accordingly, if the probability of points of failure for all aligners ina set are below the lower threshold, the method proceeds to block 118and a first manufacturing flow is determined for that aligner set. Thefirst manufacturing flow may be, for example, a fast track manufacturingflow. The fast track manufacturing flow may operate under the assumptionthat no exceptions will be performed, that no aligners in thatmanufacturing flow will undergo rework, and that the manufacture may becompleted with minimal waiting in embodiments. However, if any alignersin an aligner set have any points with a probability of failure/damagethat meets or exceeds the lower threshold, the method may continue toblock 120.

In some embodiments, processing logic selects from two possiblemanufacturing flows, and the operations of block 116 are skipped, withthe method proceeding from block 114 to block 120.

At block 120, each of the one or more data sets is assessed to determinewhether any of the aligners in any of the data sets has a probability ofdamage/failure that is at or above an upper probability threshold. Theupper threshold may have, for example, a value of a 45%, 50%, 55%, 60%,or 65% chance of a point of damage/failure. Aligner sets that have atleast one aligner with at least one point having a probability ofdamage/failure that meets or exceeds the upper threshold may beidentified as particularly high risk aligner sets. Such high riskaligner sets may be subject to increased scrutiny, slower manufacturing,added quality control steps, and so on, which may reduce the chance ofthe aligners in the set becoming damaged and/or increase a chance ofdetecting any damage in such aligner sets. Accordingly, if no alignersin an aligner set have any points with a probability of damage/failureat or above the upper threshold, the method continues to block 122, anda second manufacturing flow may be selected. If the probability ofpoints of failure for one or more aligners in a set are above the upperthreshold, the method proceeds to block 124 and a third manufacturingflow is determined for that aligner set. The second manufacturing flowmay be a standard manufacturing flow for aligners. The thirdmanufacturing flow may be a quality control manufacturing flow (e.g.,that examines some or all of the aligners in the aligner set using aninspection station for image-based quality control). The thirdmanufacturing flow may be performed by the most experienced techniciansor operators in embodiments. In one embodiment, a cycle time for thethird manufacturing flow is increased to provide an operator additionaltime to carefully handle the aligners (e.g., to remove aligners frommolds). The first manufacturing work flow at block 118 may be a workflow with a lowest complexity. The second manufacturing work flow atblock 122 may be a work flow with an intermediate level of complexity.The third manufacturing work flow at block 124 may be a work flow with amaximum level of complexity.

FIG. 2A illustrates a flow diagram for a method 200 of training amachine learning model to perform analysis on a digital design of analigner, in accordance with one embodiment. The machine learning modelmay be trained to predict whether an orthodontic aligner will be damagedduring manufacturing of the orthodontic aligner, in accordance with oneembodiment.

One or more operations of method 200 are performed by processing logicof a computing device. The processing logic may include hardware (e.g.,circuitry, dedicated logic, programmable logic, microcode, etc.),software (e.g., instructions executed by a processing device), firmware,or a combination thereof. For example, one or more operations of method200 may be performed by a processing device executing an aligner designanalysis module 1450 of FIG. 14.

At block 202 of method 200, processing logic may preprocess digitaldesigns for a plurality of orthodontic aligners so that the digitaldesigns may be used as training data for training a machine learningmodel. Some digital designs for orthodontic aligners may be associatedwith orthodontic aligners that have already been manufactured. For suchdigital designs, a clinical data store may store information indicatingwhether or not each of the associated respective orthodontic alignerswas damaged during manufacturing. Other digital designs for orthodonticaligners may be associated with orthodontic aligners that have not yetbeen manufactured. Accordingly, there may be no information regardingwhether orthodontic aligners associated with such digital designs weredamaged during manufacturing.

In one embodiment, blocks 204-208 relate to preparing digital designs oforthodontic aligners that have not been manufactured (or for whichdamage information does not exist) for use in training a machinelearning model. At block 204, processing logic may process digitaldesigns for one or more orthodontic aligners using one or more numericalsimulations to determine probable points of damage to the respectiveorthodontic aligners. Any of the numerical simulations described hereinmay be used to determine the probable points of failure/damage.Accordingly, probable points of damage for a digital design of analigner may be determined by processing the digital design of the modelusing one or more of the methods set forth in FIGS. 3A-8C inembodiments.

As discussed above and further discussed below with reference to FIGS.3A-5B a numerical simulation may be performed on the digital design ofthe aligner to simulate one or more forces and/or displacements on thealigner. In some embodiments, the forces simulate removing the alignerfrom a dental arch-like structure (e.g., teeth or the mold). Thenumerical simulation can determine when an amount of force required toremove the aligner from a dental arch-like structure reaches a value ofstress or strain/stress or deformation energy, or deformation energylevel at any point on the aligner that exceeds a threshold value, whichmay indicate that the particular point will fail. A strain may bedetermined based on a displacement, motion, or geometry change at thepoints, and the stress may be determined based on force applied to thealigner. In some embodiments, a strain or stress threshold may be usedduring the numerical simulation to determine when a point on the digitaldesign of the aligner will likely fail. In this way, the numericalsimulation may operate as a predictive model that predicts probablepoints of damage on the digital design of the aligner. These simulationsmay be run numerous times on multiple digital designs of aligners andlabels may be included with the digital designs indicating whether ornot the digital designs include one or more probable points of damage.

At block 206, processing logic may determine, for each of the digitaldesigns, whether probable points of damage are predicted for theassociated respective orthodontic aligners. At block 208, processinglogic may add information about the probable points of damage to thedigital designs for the respective orthodontic aligners. In someinstances, this may include adding information about the locations ofthe probable points of failure and/or the probability of damage/failurefor each of the points of probable failure. Additionally, processinglogic may add information about the lack of probable points of failurefor digital designs for orthodontic aligners that do not have anyprobable points of failure. In embodiments, probable points of failuremay be those points on an orthodontic aligner with a probability ofdamage that exceeds a probability threshold, such as 50%, 60%, or someother value. The probable points of failure, and lack of probable pointsof failure, may serve as labels for digital designs of orthodonticaligners. For example, digital designs for which one or more probablepoints of failure are identified may be assigned a label of 1,indicating a prediction that the associated aligner will be damagedduring manufacture. Digital designs for which no probable points offailure are identified may be assigned a label of 0, indicating aprediction that the associated aligner will not be damaged duringmanufacture.

In one embodiment, blocks 210-216 relate to preparing digital designs oforthodontic aligners that have been manufactured, and for which damageinformation exists, for use in training a machine learning model. Atblock 210, processing logic may receive digital designs for one or moreorthodontic aligners. At block 212, processing logic may receiveinformation indicating one or more of the orthodontic aligners that weredamaged during manufacturing. Additionally, processing logic may receiveinformation indicating one or more locations at which damage occurred inmanufactured aligners and/or types of damage that occurred (e.g.,warping, cracking, deformation, etc.). Actual points of damage foraligners may be reported by manufacturing technicians, by an automatedmanufacturing system and/or by patients in some embodiments.

The information pertaining to whether the aligners experienced points ofdamage may also be obtained from historical patient feedback. Forexample, patients may provide a report that specifies the aligner failedand/or the location of the damage may be determined (e.g., from thereport, from scanning the aligner, etc.). Also, the patient may specifywhich aligner (e.g., top or bottom) at a particular stage of thetreatment plan failed. In some instances, the patient may return thebroken aligner to a site and the broken aligner may be scanned at thesite to obtain an image of the digital design of the polymeric alignerincluding the location of the point of damage. As such, images of thebroken aligners may be collected for image corpora (a set of imagecorpus, which may include a large set of images) and used as part of thetraining data. Information provided by the patient about the brokenaligner or determined via scanned images may be correlated to determinethe ID of the aligner, which can then be used to obtain the digitaldesign of that particular aligner. The location of the point of damagemay be placed in the digital design of the aligner with a labelindicating there is a point of damage at that location.

At block 216, processing logic may add information about whether damageoccurred (e.g., about points of damage) to the digital designs for therespective orthodontic aligners. In some instances, this may includeadding information about the locations of detected points offailure/damage. Additionally, processing logic may add information aboutthe lack of damage for digital designs for orthodontic aligners thatwere not damaged during manufacturing. The probable points of damage,and lack of points of damage, may serve as labels for digital designs oforthodontic aligners. For example, digital designs for which damageoccurred may be assigned a label of 1, indicating that the associatedaligner was damaged during manufacture. Digital designs for which nodamage occurred may be assigned a label of 0, indicating that theassociated aligner was not damaged during manufacture. Accordingly,actual points of damage on physical aligners may be added as labels ormetadata to the associated digital designs of the aligners. In someinstances, digital aligners are labeled with information indicatingwhether or not the associated physical aligners had one or more damagedpoints, but the actual locations of the damaged points are notindicated.

At block 218, processing logic may extract at least one of geometricalcharacteristics, treatment related characteristics or clinicalcharacteristics from the digital designs of the orthodontic aligners. Inone embodiment, the characteristics are extracted by a software modulethat analyzes three dimensional virtual models of dental arches and/oraligners, and that determines characteristics of the associated dentalarches and/or aligners based on the analysis. The extractedcharacteristics may include many different characteristics, includingcharacteristics that have no bearing on whether an aligner will becomedamaged as well as characteristics that may have some effect on whetheran aligner will become damaged. Examples of geometrical characteristicsinclude individual tooth shape for one or more teeth, location of teethon a dental arch in relation to other teeth, jaw shape, and so on.Examples of treatment related characteristics include number of stagesof treatment, number and positions of attachments to teeth, whetheraligners are active or passive aligners, and so on. Examples of clinicalcharacteristics include amount of tooth crowding, deep bite, level ofmalocclusion, and so on. In embodiments, the characteristics that areextracted by processing logic may be formatted as structured or tabulardata. Accordingly, characteristics about the aligner associated with adigital design may be represented as structured or tabular data.

At block 220, a subset of the characteristics for each digital designmay be selected. In one embodiment, the same characteristics areincluded the subsets for each of the digital designs. The subset ofselected characteristics may be those characteristics that correlate todamage or manufacturing defects in aligners.

Table 1 below identifies numerous characteristics that may be extractedfrom a digital model of a dental arch or a digital model of an aligner,in accordance one embodiment. Table 1 further indicates, for oneembodiment, whether each characteristic was included in the subset atblock 220. Table 1 shows just a small sample of the many different typesof characteristics that may be extracted from a digital model of adental arch and/or a digital model of an aligner. While a majority ofthose characteristics that are shown are included in the subset, in someembodiments less than half (e.g., just a small fraction) of the totalnumber of extracted characteristics may be included in the subset.

In Characteristics Description of characteristics subset? Active alignercount Number of active aligners (integer) Yes Left molar shift Leftmolar's shift from ideal Class1 position divided by distance Yes betweenideal BiteClass2 and ideal BiteClass1 (%) Left canine shift Leftcanine's shift from ideal Class1 position divided by distance No betweenideal BiteClass2 and ideal BiteClass1 (%) Right molar shift Rightmolar's shift from ideal Class1 position divided by distance Yes betweenideal BiteClass2 and ideal BiteClass1 (%) Right canine shift Rightcanine's shift from ideal Class1 position divided by distance No betweenideal BiteClass2 and ideal BiteClass1 (%) Canine average tooth widthAverage width of canine teeth (mm) Yes Canine average tooth heightAverage height of canine teeth (mm) Yes Canine ridge count Total numberof ridges on canines (integer) No Canine depth delta Delta betweeninitial depth and planned depth for a canine (mm) Yes Canine maximumangulation Maximum tooth angulation of canines in one or more axes Yes(degrees) Canine maximum inclination Maximum tooth inclination ofcanines (degrees) Yes Incisor attachment count Total number ofattachments on incisors (integer) Yes Incisor average crown heightAverage height of crown height of incisors (mm) Yes Incisor maximumangulation Maximum tooth angulation of incisors in one or more axes Yes(degrees) Incisor maximum inclination Maximum tooth inclination ofincisors (degrees) Yes Canine maximum Absolute distance between toothfront point and jaw arch along jaw Yes prominence occlusal plane forcanines (mm) Incisor maximum Absolute distance between tooth front pointand jaw arch along jaw Yes prominence occlusal plane for incisors (mm)Molar attachment count Total number of attachments on molars (integer)Yes Molar average crown height Average height of crown height of molars(mm) Yes Molar maximum prominence Absolute distance between tooth frontpoint and jaw arch along jaw Yes occlusal plane for molars (mm) Passivealigner count Number of passive aligners (integer) Yes Final premolarcrowding Final premolar crowding minus sum of collision depths for allteeth Yes pairs between first premolars of given jaw Initial premolarcrowding Initial premolar crowding minus sum of collision depths for allteeth Yes pairs between first premolars of given jaw Premolar attachmentcount Total number of attachments on premolars (integer) Yes Premolaravg. crown height Average height of crown height of premolars (mm) YesPremolar max angulation Maximum tooth angulation of premolars in one ormore axes Yes (degrees) Incisor max inclination Maximum toothinclination of premolars (degrees) Yes Intermolar distance Distancebetween leftmost and rightmost back molars (mm) Yes Spee curve formolars Spee curve depth for molars Yes

One possible extracted characteristic is the Spee curve (also referredto the curve of Spee), which is the curvature of the mandibular occlusalplane beginning at the premolar and following the buccal cusps of theposterior teeth, continuing to the terminal molar. In other words, theSpee curve is an anatomic curvature of the occlusal alignment of theteeth, beginning at the tip of the lower incisor, following the buccalcusps of the natural premolars and molars, and continuing to theanterior border of the ramus. The idea behind measuring this curvatureis to find a circle in the sagittal plane in 2D space or to find asphere in 3D space that best fits a set of tip points of the lower jaw.The radius and the angle between the segments connecting the center ofthis circle with the tip point of the terminal molar and the firstincisor may be measures of curvature. It may be assumed that the largerthe radius of the circle and the smaller the angle, the less pronouncedthe curvature of the jaw.

For finding the Spee curve in 2D space, the curvature may be measuredseparately for each side of the jaw arch. Each tip point may beprojected onto a jaw midline plane (e.g., where the x coordinate equalszero). The problem of finding the center and the radius of the circlethat best fits all the points may be solved as follows:

-   -   1) Compute an initial guess by averaging the x and y coordinates        for all points;    -   2) Improve on the initial guess, such as by using a least        squares estimator (e.g., based on the

Euclidean distance between the points and the circle); and

-   -   3) Given computed residuals and a cost function, use least        squares to final a local minimum of the cost function (e.g.,        using the Levenberg-Marquardt method) and return the circle's        radius and coordinates of the center of the circle. Processing        logic may then find an angle between the segments connecting the        center of the circle with the tip point of the terminal molar        and the first incisor.

At block 222, processing logic may generate an embedding for eachdigital design for an orthodontic aligner based on the subset of thecharacteristics determined for that digital design. The embedding mayhave a structured or tabular data format in some embodiments.

In an alternative embodiment, the operations of block 218 and 220 maynot be performed. Instead, one or more height maps may be generated fromthe digital design for the aligners (e.g., from the 3D digital model ofthe dental arch or of the aligner). The height maps may be generated byprojecting the 3D digital model onto multiple different planes frommultiple different perspectives. In such an embodiment, at block 222 theembeddings may be generated by combining the multiple height mapsassociated with a digital design for an aligner.

At block 224, processing logic gathers a training dataset comprisingdigital designs of a plurality of orthodontic aligners. The trainingdataset may include the embeddings generated at block 222 in anembodiment. Each embedding may be associated with metadata indicatingwhether the aligner associated with the embedding is labeled as adamaged aligner or as an undamaged aligner. The training datasetpreferably contains thousands, tens of thousands, hundreds of thousandsor more data points, where each data point is data (e.g., an embedding)associated with a different aligner. Digital designs of aligners withassociated points of damage (as provided by real world data) and digitaldesigns of aligners with associated probable points of damage (asprovided by an output of a numerical simulation) may be used together togenerate a robust machine learning model that can predict probablepoints of damage of new aligners from digital models of those alignersin some embodiments. The machine learning model or statistical model mayalso classify types of damage, degree of damage, and/or otherinformation related to aligners in embodiments.

At block 226, processing logic trains a machine learning model using thetraining dataset. The machine learning model may be trained to processdata (e.g., an embedding) from a digital design for an orthodonticaligner and to output a probability that the orthodontic alignerassociated with the digital design will be damaged during manufacturingof the orthodontic aligner, will be damaged during clinical usage of theorthodontic aligner, will be damaged during shipping and handling of theorthodontic aligner, etc. In embodiments, the machine learning model istrained to have a rate of false positives to a desired target, forexample 2% or less.

A machine learning model may refer to a model artifact that is createdby a training engine using a training dataset (e.g., training input andcorresponding target outputs or labels). Training may be performed usinga set of training data including at least one of a) digital designs of afirst set of aligners with labels indicating whether or not each of thefirst plurality of aligners experienced one or more points of damage orb) digital designs of a second set of aligners with labels indicatingwhether or not each of the second set of aligners include one or moreprobable points of damage. The machine learning model may be composed ofa single level of linear or non-linear operations (e.g., a supportvector machine (SVM) or a single level neural network) or may be a deepneural network that is composed of multiple levels of non-linearoperations. Examples of deep networks and neural networks includeconvolutional neural networks and/or recurrent neural networks with oneor more hidden layers. Some neural networks may be composed ofinterconnected nodes, where each node receives input from a previousnode, performs one or more operations, and sends the resultant output toone or more other connected nodes for further processing.

Convolutional neural networks include architectures that may provideefficient image recognition. Convolutional neural networks may includeseveral convolutional layers and subsampling layers that apply filtersto portions of the image of the text to detect certain features (e.g.,points of damage). That is, a convolutional neural network includes aconvolution operation, which multiplies each image fragment by filters(e.g., matrices) element-by-element and sums the results in a similarposition in an output image.

Recurrent neural networks may propagate data forwards, and alsobackwards, from later processing stages to earlier processing stages.Recurrent neural networks include functionality to process informationsequences and store information about previous computations in thecontext of a hidden layer. As such, recurrent neural networks may have a“memory”.

In some embodiments, the machine learning model may be a random forestclassifier. A random forest classifier applies an ensemble learningmethod for classification by constructing multiple decision trees (e.g.,hundreds to thousands of decision trees) during training that outputclassification decisions based on input data. A random forest classifieraverages the decisions of multiple decision trees, and produces outputsbased on the average. Different decision trees in the random forestclassifier may be trained on different parts of the training dataset inembodiments. Each decision tree may be a predictive model that usesobservations about input data (represented in branches of the decisiontree) to reach a conclusion about the input data (represented in leavesof the decision tree). For example, each decision tree may be trained todetermine a classification for a digital design for an aligner. Inembodiments, the random forest classifier may be trained using atraining algorithm such as feature bagging (also referred to asbootstrap aggregating) that selects, at each candidate split in thelearning process, a random subset of features. An advantage of a trainedrandom forest classifier is that after a classification is made,processing logic or a user can determine exactly why the classificationwas made by following the branches of the one or more decision treesthat reached the classification decision.

In some embodiments, the machine learning model may be an XGBoostclassifier. An XGBoost classifier is an implementation of a gradientboosted decision tree. In other embodiments, other gradient boosteddecision trees may be used to implement the machine learning model.Boosting is an ensemble technique where new models are added to correctthe errors made by existing models. Models are added sequentially untilno further improvernents can be made. Gradient boosting is an approachwhere new models are created that predict the residuals or errors ofprior models. Results of multiple models are then added together to makea final prediction. lt is called gradient boosting because it uses agradient descent algorithm to minimize the loss when adding new models.In some embodiments, the machine leaning model may be a logisticregression model.

In embodiments in which a random forest classifier or gradient boosteddecision tree classifier (e.g., XGBoost classifier) are trained oncharacteristics extracted from digital models of dental arches oraligners, the machine learning model may be trained to express the jointeffect of the characteristics and identify aligners that are likely tobe damaged or broken.

In some embodiments, the machine learning model may be periodicallyretrained using updated training datasets. For example, additional dataon manufactured aligners may be continuously generated as new patientsare treated. On some periodic or regular basis (e.g., every six months),processing logic may repeat the training of the machine learning model.By regularly retraining the machine learning model, new information,techniques and/or processes may be captured and reflected in the machinelearning model, such as updated software, updated manufacturing flows,and so on. In some embodiments, training of the machine learning modelmay be ongoing or continuous based on a continuous inflow of new data.In some embodiments, different machine learning models are trained foraligners that are formed from different materials, for aligners that aremanufactured using different manufacturing flows, and/or for alignersthat have other parameters (e.g., direct fabrication vs. thermoforming).For example, a first machine learning model may be trained to predictprobable points of damage on an aligner that is manufactured bythermoforming it over a mold, and a second machine learning model may betrained to predict probably point of damage on an aligner that isdirectly fabricated using 3D printing or other rapid prototypingtechniques.

FIG. 2B illustrates a flow diagram for a method 230 of performinganalysis on a digital design of an aligner using a trained machinelearning model, in accordance with one embodiment. One or moreoperations of method 230 are performed by processing logic of acomputing device. The processing logic may include hardware (e.g.,circuitry, dedicated logic, programmable logic, microcode, etc.),software (e.g., instructions executed by a processing device), firmware,or a combination thereof. For example, one or more operations of method230 may be performed by a processing device executing an aligner designanalysis module 1450 of FIG. 14. It should be noted that the method 230may be performed for each unique aligner for each patient's treatmentplan, or for each unique aligner at key stages of the treatment plan.Further, method 230 includes operations that may be performed duringblock 104 of FIG. 1A.

At block 232 of method 230, processing logic may perform an analysis ona digital design of an orthodontic aligner (e.g., a polymericorthodontic aligner) using a trained machine learning model, which mayhave been trained in accordance with method 200. Performing the analysison the digital design of the aligner using the trained machine learningmodel may include applying (block 234) the digital design of the alignerto the trained machine learning model as an input. Further, performingthe analysis on the digital design of the aligner using the trainedmachine learning model may include generating (block 236), by thetrained machine learning model, an output indicating whether the digitaldesign of the aligner includes the one or more probable points ofdamage. If the digital design of the aligner includes the one or moreprobable points of damage, the output of the trained machine learningmodel may identify the locations of the one or more points of damage insome embodiments. The output of the trained machine learning model mayadditionally include recommendations of one or more of the correctiveactions described above. Alternatively, the output of the trainedmachine learning model may be input into a further system or module(e.g., another trained machine learning model) along with the digitaldesign of the aligner. The further system or module may then determine arecommended corrective action based on the digital design of the alignerand the predicted point(s) of damage.

After the trained machine learning model determines that one or morepoints of probable damage are predicted, the digital design of thealigner that includes the one or more probable points of damage may befurther processed by performing a numerical simulation on the digitaldesign of the polymeric aligner to verify whether the one or moreprobable points of damage are present in some embodiments. The numericalsimulation may be any of the numerical simulations described herein. Forexample, the numerical simulation may a) simulate removal of theorthodontic aligner from a mold of a dental arch of a patient or b)simulate loading around weak spots in the orthodontic aligner inembodiments. Processing the digital model of the aligner using thenumerical simulation may be computationally expensive and require muchgreater resources than processing the digital model of the aligner usingthe trained machine learning model. Accordingly, by first processing thedigital model of the aligner using the trained machine learning model,and then limiting the use of the numerical simulation to testing digitalmodels of aligners for which the trained machine learning modelpredicted a point of damage, resource utilization (e.g., memory and/orprocessor utilization) may be minimized. Additionally, in someembodiments the trained machine learning model determines the presenceof one or more probable points of damage, but does not identify thelocation of such probable points of damage. By processing digital modelsof aligners for which the trained machine learning model has predicted apoint of damage using the numerical simulation, the locations of the oneor more points of damage may be identified, and corrective actions maybe determined in some embodiments.

FIG. 2C illustrates a flow diagram for a method 240 of determiningwhether an orthodontic aligner will become damaged (e.g., break) duringor after manufacturing of the orthodontic aligner using a trainedmachine learning model, in accordance with one embodiment. Examples ofpost-manufacturing damage include damage during clinical use of thealigner, damage during shipping and handling of the aligner, and so on.The machine learning model may have been trained according to method200. One or more operations of method 240 are performed by processinglogic of a computing device. The processing logic may include hardware(e.g., circuitry, dedicated logic, programmable logic, microcode, etc.),software (e.g., instructions executed by a processing device), firmware,or a combination thereof. For example, one or more operations of method240 may be performed by a processing device executing an aligner designanalysis module 1450 of FIG. 14. It should be noted that the method 240may be performed for each unique aligner for each patient's treatmentplan, or for each unique aligner at key stages of the treatment plan.Further, method 230 includes operations that may be performed duringblock 104 of FIG. 1A.

At block 242 of method 240, processing logic may extract geometricalcharacteristics, treatment related characteristics and/or clinicalcharacteristics from a digital design of an orthodontic aligner in themanner set forth above with reference to method 200. At block 244,processing logic may select a subset of the characteristics. The subsetof characteristics that are selected may correspond to a same subset ofcharacteristics that were used to train the machine learning model. Atblock 246, processing logic may generate an embedding for the digitaldesign based on the subset of the characteristics.

At block 248, processing logic processes data from the digital design ofthe orthodontic aligner using the trained machine learning model. Thedata from the digital design may include the embedding generated atblock 246 in an embodiment. Alternatively, or additionally, the datafrom the digital design may include a three dimensional digital model ofthe aligner or a three dimensional digital model of a dental arch ormold to be used to manufacture the aligner. Alternatively, oradditionally, the data from the digital design may include one or moreheight maps that are generated by projecting the three dimensionaldigital model of the dental arch or the aligner onto one or more planes.

At block 250, the trained machine learning model outputs a probabilitythat the orthodontic aligner associated with the digital model will bedamaged during manufacturing of the aligner or during later use of thealigner. The probability may be a value ranging from 0 to 1, where 1 mayrepresent a 100% chance that the aligner will be damaged and a 0represents a 0% chance that the aligner will be damaged.

In one embodiment, at block 252 the machine learning model furtheroutputs information identifying the probability that specific points orlocations of the orthodontic aligner will be damaged. For example, aseparate probability value from 0 to 1 may be output for each of aplurality of points on the orthodontic aligner.

In one embodiment, at block 254 processing logic determines whether theprobability of the orthodontic aligner being damaged is below a firstthreshold (or whether the probability of all points on the orthodonticaligner being damaged are below the first threshold). If the probabilityof the orthodontic aligner being damaged is below the first threshold,the method continues to block 256, and a determination may be made thatthe aligner is a low risk aligner. As in FIG. 1B, a first manufacturingflow for low risk aligners may then be selected for the aligner.

If at block 254 a determination is made that the probability of theorthodontic aligner is above the first threshold, the method continuesto block 256. At block 256, processing logic determines whether theprobability of the orthodontic aligner being damaged is above a secondthreshold (or whether the probability of any points on the orthodonticaligner being damaged are above the second threshold). The secondthreshold may be above the first threshold. For example, the firstthreshold may be 0.2%, 0.5%, 1%, 2%, 5%, of 10%, and the secondthreshold may be 15%, 20%, 25%, 30%, 40%, or 50%. If the probability ofthe orthodontic aligner being damaged is above the second threshold, themethod continues to block 260. Otherwise, the method continues to block258.

At block 258, a determination may be made that the aligner is a standardrisk aligner. As in FIG. 1B, a second manufacturing flow for standardrisk aligners may then be selected for the aligner.

At block 260, processing logic determines that the aligner is a highrisk aligner. As in FIG. 1B, a third manufacturing flow for high riskaligners may then be selected for the aligner. In one embodiment, atblock 262 processing logic may output a notification comprising alocation of at least one point with a probability of damage at or abovethe second threshold. Such a notification may be output, for example, ifthe machine learning model output data indicating locations of points onthe aligner and associated probabilities of those points becomingdamaged.

In some embodiments, as shown in FIG. 2C, three differentclassifications may be determined for an aligner based on theprobability that the aligner will be damaged during manufacturing orafter manufacturing. These may include a low risk classification, amedium or standard risk classification, and a high risk classification.In other embodiments, aligners may be classified into a binaryclassification, including standard risk (or no damage predicted) andhigh risk (or damage predicted). In such embodiments, the operations ofblocks 254 and 256 may be omitted.

FIG. 2D illustrates a flow diagram for a method 264 of determiningwhether any orthodontic aligner in a set of orthodontic alignersassociated with a treatment plan for a patient will become damaged(e.g., break) during or after manufacturing of the set of orthodonticaligners using a trained machine learning model, in accordance with oneembodiment. The machine learning model may have been trained accordingto method 200. One or more operations of method 264 are performed byprocessing logic of a computing device. The processing logic may includehardware (e.g., circuitry, dedicated logic, programmable logic,microcode, etc.), software (e.g., instructions executed by a processingdevice), firmware, or a combination thereof. For example, one or moreoperations of method 264 may be performed by a processing deviceexecuting an aligner design analysis module 1450 of FIG. 14. It shouldbe noted that the method 264 may be performed for each treatment plan,or for the upper dental arch and lower dental arch of each treatmentplan.

At block 266 of method 264, processing logic determines an aligner setcomprising digital designs for orthodontic aligners associated with atreatment plan for a patient. For example, a treatment plan may divideorthodontic treatment of a patient into a sequence of stages, and adifferent orthodontic aligner may be designed for each stage oftreatment. A single treatment plan may include any number of stages andassociated digital designs for orthodontic aligners (e.g., up to 50stages), and separate digital designs may be generated for the upper andlower dental arches for each stage. In one embodiment, the aligner setincludes all of the digital designs for either the upper dental arch orthe lower dental arch associated with a treatment plan for a patient. Inone embodiment, the aligner set includes all digital designs of both theupper dental arch and the lower dental arch associated with thetreatment plan for a patient.

At block 268, processing logic may extract geometrical characteristics,treatment related characteristics and/or clinical characteristics fromthe digital design of each orthodontic aligner in the aligner set in themanner set forth above with reference to method 200. At block 270,processing logic may select a subset of the characteristics. The subsetof characteristics that are selected may correspond to a same subset ofcharacteristics that were used to train the machine learning model. Atblock 272, processing logic may generate an embedding for each digitaldesign in the aligner set based on the respective subset of thecharacteristics.

At block 274, processing logic processes data from the digital designsof the orthodontic aligners using the trained machine learning model.The data from the digital designs may include the embeddings generatedat block 246 in an embodiment. Alternatively, or additionally, the datafrom the digital designs may include three dimensional digital models ofthe aligners or three dimensional digital models of a dental arch ormold to be used to manufacture the aligners. Alternatively, oradditionally, the data from the digital designs may include one or moreheight maps that are generated by projecting the three dimensionaldigital models of the dental arch or the aligner onto one or moreplanes.

At block 276, the trained machine learning model outputs, for eachdigital design of an aligner in the aligner set, a probability that thealigner associated with the respective digital model will be damaged(e.g., during manufacturing of the aligner or during later use of thealigner). The probability may be a value ranging from 0 to 1, where 1may represent a 100% chance that the aligner will be damaged and a 0represents a 0% chance that the aligner will be damaged.

In one embodiment, at block 278 processing logic determines whether theprobability of any orthodontic aligner being damaged is below a firstthreshold (or whether the probability of being damaged for all points onthe orthodontic aligners are below the first threshold). If theprobability of being damaged is below the first threshold for all theorthodontic aligners, the method continues to block 280, and adetermination may be made that the aligner set is a low risk alignerset. As in FIG. 1B, a first manufacturing flow for a low risk alignerset may then be selected for the aligner set.

If at block 278 a determination is made that the probability of one ormore orthodontic aligner being damaged is above the first threshold, themethod continues to block 282. At block 282, processing logic determineswhether the probability of at least one orthodontic aligner beingdamaged is at or above a second probability threshold (or whether theprobability of any points on at least one orthodontic aligner beingdamaged are at or above the second threshold). The second threshold maybe above the first threshold. For example, the first threshold may be0.2%, 0.5%, 1%, 2%, 5%, of 10%, and the second threshold may be 15%,20%, 25%, 30%, 40%, or 50%. If the probability of any orthodonticaligner in the aligner set being damaged is at or above the secondthreshold, the method continues to block 286. Otherwise, the methodcontinues to block 284.

At block 284, a determination may be made that the aligner set is astandard risk aligner set. As in FIG. 1B, a second manufacturing flowfor standard risk aligner sets may then be selected for the aligner set.

At block 286, processing logic determines that the aligner set is a highrisk aligner set. As in FIG. 1B, a third manufacturing flow for highrisk aligner sets may then be selected for the aligner set.

In some embodiments, as shown in FIG. 2D, three differentclassifications may be determined for an aligner set based on theprobability that aligners in the aligner set will be damaged duringmanufacturing or after manufacturing. These may include a low riskclassification, a medium or standard risk classification, and a highrisk classification. In other embodiments, aligner sets may beclassified into a binary classification, including standard risk (or nodamage predicted) and high risk (or damage predicted). In suchembodiments, the operations of blocks 254 and 256 may be omitted.

FIG. 3A illustrates a flow diagram for a method 300 of performinganalysis on a digital design of an aligner (e.g., a polymeric aligner)using numerical simulation, in accordance with one embodiment. One ormore operations of method 300 are performed by processing logic of acomputing device. The processing logic may include hardware (e.g.,circuitry, dedicated logic, programmable logic, microcode, etc.),software (e.g., instructions executed by a processing device), firmware,or a combination thereof. For example, one or more operations of method300 may be performed by a processing device executing an aligner designanalysis module 1450 of FIG. 14. It should be noted that the method 300may be performed for each unique aligner for each patient's treatmentplan, or for each unique aligner at key stages of the treatment plan.Further, method 300 includes operations that may be performed duringblock 104 of FIG. 1A.

At block 302, processing logic may perform the analysis on the digitaldesign of the aligner using numerical simulation associated with removalof the polymeric aligner from tooth-like or dental arch-like structures(such as the mold or patient dentition). The numerical simulation mayinclude finite element method, finite difference method, finite volumemethod, meshfree methods, smoothed-particle methods, combinations ofthese methods, or the like. Finite element method (also referred to asfinite element analysis) may refer to a numerical method for solvingpartial differential equations, which can also be applied to performstructural analyses of aligners. The geometry of structure (in this casealigner) is discretized to a number of points or elements over a domainto solve a set of partial differential equations characterizing theconstitutive relations of the aligner material, and solutions areexplored in the finite dimensional functional space. Finite differencemethod may refer to a numerical method for solving differentialequations by approximating them with difference equations andcalculating approximate values at discrete points. Finite volume methodmay refer to a method for representing and evaluating partialdifferential equations in the form of algebraic equations. Finite volumemethod may also calculate values (e.g., strain, stress, force) atdiscrete places on a meshed geometry of the digital design of thealigner. “Finite volume” may refer to the small volume surrounding eachpoint on a mesh. Meshfree methods may refer to methods that are based oninteraction of nodes or points with all of the neighboring nodes orpoints. In other words, meshfree methods do not require connectionbetween nodes of the simulation domain. The smoothed-particle Galerkinor hydrodynamics method may be forms of meshfree methods.

At block 304, processing logic may simulate one or more forces and/ordisplacements on the digital design of the aligner that are associatedwith removal of the aligner from the dental arch-like structure (e.g.,mold or the dental arch of the patient). Simulating the one or moreforces and/or displacements on the digital design of the aligner mayinclude performing operations at blocks 306, 308, 310, 312, and 314. Atblock 306, processing logic may gather one or more material properties(also referred to as material property information) of the aligner. Thematerial properties may include an amount or value of stress and/orstrain that the material can sustain before cracking, breaking,deforming, warping, etc. One example of a material property of thematerial is the Young's Modulus of the material. In some embodiments,the material properties may not change between different digital designsof aligners because the aligners will be made of the same material(e.g., polymeric). Material properties may be included in aconfiguration of the aligner design analysis module 1450 in embodiments.

At block 308, processing logic may gather a first geometry of thealigner from the digital design of the aligner. The first geometry maybe specific to each patient (and to each stage of treatment) and may bedetermined based on the dental arch of the patient. The first geometrymay be obtained by generating the digital design of the aligner bymanipulating a digital model of a dental arch-like structure (e.g., of amold or dental arch of a patient). The digital model of the dentalarch-like structure may represent the dental arch of the patient. Thedigital model of the mold may be offset to approximate a surface of thealigner and to generate the digital design of the aligner. As such, thedigital design of the aligner may include cavities configured to receiveteeth (referred to as tooth-receiving cavities or caps) of the patientand/or attachments on the teeth.

At block 310, processing logic may gather a second geometry of thedental arch-like structure from a digital model of the dental arch-likestructure (e.g., mold). The digital model of the dental arch-likestructure may be generated from information obtained by performing anintraoral scan of the patient during a consultation and/or from atreatment plan. For example, the dental arch of the patient may bedigitized, via scanning, and modeled as the dental arch used tofabricate the mold. The second geometry may include information relatedto the dental arch of the patient, such as the tooth size, tooth shape,tooth orientation, distance between teeth, attachments on teeth, upperdental arch, lower dental arch, etc.

At block 312, processing logic may simulate the removal of the alignerhaving the one or more material properties and the first geometry fromthe dental arch-like structure having the second geometry by applyingthe one or more loads (e.g., one or more forces and/or displacements) toa set of points on the digital design of the aligner. The numericalsimulation performed may include solving a series of partialdifferential equations that model applying one or more loads (e.g.,forces and/or displacements) to the aligner having the materialproperties and the first geometry to remove the aligner from the dentalarch-like structure having the second geometry. Further, the partialdifferential equations may calculate a stress or strain value at eachpoint of the set of points on the digital design of the aligner and adetermination may be made based on the stress or strain value calculatedand the amount of force applied whether the point is a probable point ofdamage. The partial differential equations may be elastostatic orelastodynamic partial differential equations that calculate stress orstrain states within the digital design of the aligner, and thus,predict breakage, warpage, deformation, etc. High polymericstrains/stresses may be factors that cause crack initiation andbreakage, as well as warpage, deformation, and the like, in polymericaligners. The partial differential equations may be represented asfollows:

Find u_(i) (u∈

²) such that:

${{\rho \frac{\partial^{2}u_{i}}{\partial t^{2}}} = {\sigma_{{ij},j} + {f_{i}\mspace{14mu} {in}\mspace{14mu} \Omega \times \left\lbrack {0,T} \right\rbrack}}},i,{j = 1},2,3$

With boundary conditions:

u _(i)(x, t)=u _(i) ^(g)(x, t) at x ∈ δΩ _(u) _(i)

σ_(ij) n _(j) =t _(i)(x, t) at x ∈ δΩ _(t) _(i)

And initial conditions:

u _(i)(x, 0)=u _(i0)(x) at x ∈ δΩ _(u) _(i)

v _(i)(x, 0)=v _(i0)(x) at x ∈ δΩ _(u) _(i)

${{Given}\mspace{14mu} u_{i}^{g}},{\overset{\_}{t}}_{i},f_{i},u_{i\; 0},v_{i\; 0},{\sigma_{ij} = {{\mathbb{C}}_{ijkl}ɛ_{kl}}},{ɛ_{kl} = {\frac{1}{2}\left( {\frac{\partial u_{k}}{\partial x_{l}} + \frac{\partial u_{l}}{\partial x_{k}}} \right)}},\rho$${{\partial\Omega} = {{\partial\Omega_{u_{i}}}\bigcup{\partial\Omega_{{\overset{\_}{t}}_{i}}}}},{{{\partial\Omega_{u_{i}}}\bigcap{\partial\Omega_{{\overset{\_}{t}}_{i}}}} = \varphi},{i = 1},2,3$

Where u is the 3D displacement field, u_(i) ^(g) is the Dirichletboundary condition, t _(i) is the Neumann boundary condition, f_(i) isthe applied body force, u_(i0), v_(i0) are the initial displacement andvelocities, σ_(ij) and ε_(kl) are the stress and strain tensors,

_(ijkl) is the elasticity tensor, ρ is the material density, Ω is thedomain of interest. Note that

$\frac{\partial^{2}u_{i}}{\partial t^{2}} = 0$

can be set, and the elastostatics problem can be solved.

At block 314, for each point of the set of points, processing logic mayperform operations at blocks 316, and 318. At block 316, processinglogic may determine whether a value of the stress and/or strainsatisfies a damage criteria for each of the points by solving thepartial differential equations described above. The damage criteria maybe satisfied when the value of the stress and/or strain exceeds athreshold value. The partial differential equations may be used tocalculate a strain/stress or deformation energy value at each point ofthe set of points and an amount of resistive force involved in removingthe aligner from the mold at the point. Because the second geometry ofthe dental arch-like structure is used in the numerical simulation,information relating to the attachments may be correlated with theamount of resistive force. The resistive force associated with removingthe digital design of the aligner at the point, and information relatedto the second geometry of the dental arch-like structure of the dentalarch (tooth size, tooth shape, tooth numbers, distance between teeth,attachment types, attachment sizes, attachment numbers, etc.) associatedwith the point and the resistive force may be stored in a lookup tablein some embodiments. The lookup table may be referenced later bysimplified models that do not account for the second geometry of thedental arch-like structure. Accordingly, the lookup table may bepopulated prior to running simplified models that rely on the resistiveforce as part of their calculations, as described further below.

At block 318, processing logic may determine that the point is aprobable point of damage responsive to determining that the value of thestrain and/or stress satisfies the damage criteria (e.g., the value oflocal deformation (strains and stresses) exceeds the threshold (e.g.,1-20% strain or 0.5-20 MPa stress)). If the strain and/or stress valuecalculated at the point that results from the force exceeds thethreshold, then a crack may initiate and breakage may result, thestrain/stress or deformation energy may cause warpage of the aligner,deformation of the aligner, or the like. The threshold that is definedfor the strain/stress or deformation energy may relate to yield criteriasuch as von Mises or max/min principal stress/strain or deformationenergy that the polymeric material will fail when the strain/stress ordeformation energy value reaches a critical value, or may be anysuitable configurable threshold.

FIG. 3B illustrates an example numerical simulation 350 associated withremoval of a digital design of an aligner 352 from a digital model of adental arch-like structure 354, in accordance with one embodiment. Thenumerical simulation 350 graphically represents the solving of thepartial differential equations as one or more forces and/ordisplacements are applied to the digital design of the aligner 352 toremove the digital design of the aligner 352 from the digital model ofthe dental arch-like structure 354. As depicted, a set of points(represented as triangles in the digital model of the aligner 352) areincluded in the digital design of the aligner 352 and the partialdifferential equations calculates a stress or strain value at each ofthe points, as well as the amount of resistive force involved inremoving the digital design of the aligner 352 from the digital model ofthe dental arch-like structure (e.g., mold) 354 at that point. Thenumerical simulation 350 may use color-coded shading related to thestrain or stress value. A first color, shading or hashing may representa stress or strain value below a threshold and a second color, shadingor hashing may represent a stress or strain value that exceeds thethreshold. Any number of colors, shadings and/or hashes may be used torepresent various strain/stress or deformation energy values along ascale. For example, processing logic may calculate a strain value forpoints 356 that is below the threshold value, and thus, shade the pointsthe first color (e.g., blue) or first hashing, which indicates that thepoints 356 are not probable points of damage because their strain orstress value does not exceed the threshold value. In some embodiments,the shading may be based on the amount of resistive force involved inremoving the digital design of the aligner 352 from the digital model ofthe dental arch-like structure (e.g., mold) 354. If the amount ofresistive force exceeds a threshold value, then a probable point ofdamage may be identified and those points may be shaded the second color(e.g., red) or hashing.

FIG. 4A illustrates a flow diagram for a method 400 of performinganalysis on a digital design of an aligner (e.g., a polymeric aligner)using numerical simulation by modeling teeth and bonded attachments of adental arch as springs, in accordance with one embodiment. One or moreoperations of method 400 are performed by processing logic of acomputing device. The processing logic may include hardware (e.g.,circuitry, dedicated logic, programmable logic, microcode, etc.),software (e.g., instructions executed by a processing device), firmware,or a combination thereof. For example, one or more operations of method400 may be performed by a processing device executing an aligner designanalysis module 1450 of FIG. 14. It should be noted that the method 400may be performed for each unique aligner for each patient's treatmentplan, or for each unique aligner at key stages of the treatment plan.Further, method 400 includes operations that may be performed duringblock 104 of FIG. 1A.

At block 402, processing logic may perform the analysis on the digitaldesign of the aligner using numerical simulation associated with removalof the aligner from tooth-like or dental arch-like structures (such asthe mold or patient dentition). The numerical simulation may includefinite element analysis, finite element method, finite differencemethod, finite volume method, meshfree methods, smooth particle method,or the like.

At block 404, processing logic may simulate one or more forces and/ordisplacements on the digital design of the aligner that are associatedwith removal of the aligner from the dental arch-like structure.Simulating the one or more forces and/or displacements on the digitaldesign of the aligner may include performing operations at blocks 406and 408. At block 406, processing logic may model each tooth of thedental arch of the patient as a potentially breakable connector (e.g.,spring) attached to a respective cavity of the digital design of thepolymeric aligner. Modeling each tooth as a spring may becomputationally less expensive and time consuming than using the secondgeometry of the digital model of the mold. The modeled springs may beused to determine reaction strains and stresses and determining theeffects of those strains and stresses at portions of the digital designof the polymeric aligner. The calibration of the spring parameters canbe determined by various techniques such as experiments and moredetailed computational models.

At block 408, for each spring, processing logic may perform operationsat blocks 410, 412, 414, and 416. At block 410, processing logic maydetermine a stiffness of the spring based on the resistive forceassociated with the tooth being modeled and a geometry of the toothand/or any attachment associated with the tooth that the spring models.In some embodiments, the resistive force may be obtained from the lookuptable described above without running the numerical simulation describedwith reference to FIG. 3A that uses the second geometry of the dentalarch-like structure represented by the digital model of the dentalarch-like structure. For example, the lookup table may store informationthat the digital design of the polymeric aligner removed from aparticular tooth with 0 attachments breaks at 1 Newton (N) of appliedforce, the digital design of the polymeric aligner removed from aparticular tooth with 1 attachment breaks at 3 N of applied force, thedigital design of the polymeric aligner removed from a particular toothwith 2 attachments breaks at 5 N of applied force, etc. In someembodiments, the resistive force may be dynamically calculated using thenumerical simulation described with reference to FIG. 3A. The geometryof an attachment and associated tooth may include an undercut of theattachment and/or the tooth. The undercut of the attachment may refer toa height of a lower surface of attachment. A height of the undercut ofthe attachment can be used to determine a distance that the digitaldesign of the polymeric aligner needs to move to detach from theattachment at the tooth. The stiffness may be determined by dividing theresistive force by the distance of the undercut. The determinedstiffness may be measured in Newtons per millimeter (N/mm). For example,a connector stiffness may be 30 N/mm (3 N of resistive force divided by0.1 mm distance of the undercut).

At block 412, processing logic may determine an amount of forcenecessary to break the spring by performing the numerical simulation ofremoving the digital design of the aligner from the spring. In someembodiments, the partial differential equations described above may beused to perform the numerical simulation of removing the digital designof the aligner from the spring. In some instances, a vertical forceassociated with the spring is used in the partial differential equationsand linear operations may be used, as opposed to non-linear operationsused in the partial differential equations described with reference tomethod 300 of FIG. 3A. The partial differential equations may input thespring stiffness and/or the material properties of the aligner todetermine the required force. Also, the partial differential equationsmay compute a strain/stress or deformation energy value at points of thedigital design of the aligner that are associated with the spring whilethe removal of the digital design of the aligner from the spring isbeing simulated.

At block 414, processing logic may determine whether, during the removalprocess, the forces on the spring are greater than a threshold amount offorce. If the forces are greater than the threshold, then the spring maybreak. If the forces are greater than the threshold amount of force, oneor more strain/stress or deformation energy values at one or more pointson the digital design of the aligner may exceed a thresholdstrain/stress or deformation energy value caused by the excessive force.

At block 416, processing logic may determine that a point on the digitaldesign of the aligner is a probable point of damage responsive todetermining whether the stress/strain or deformation energy on thealigner satisfies a damage criteria. The stress/strain or deformationenergy may satisfy the damage criteria when a value of the stress/strainor deformation energy exceeds a threshold value. In an embodiment,processing logic may determine that a point on the digital design of thealigner is a probable point of damage responsive to determining that theamount of force required to break the spring associated with the pointexceeds the threshold amount of force. One or more corrective actionsmay be performed in response to determining that there is a probablepoint of damage. In some embodiments, the digital design of the alignermay be input into the trained machine learning model to verify theprobable point of damage.

FIG. 4B illustrates an example numerical simulation 450 that modelsteeth of the dental arch of the patient as springs 452, in accordancewith one embodiment. As depicted, each spring 452 is inserted into arespective cavity of a digital design of the polymeric aligner 454 justas a tooth would be when the aligner is worn or attached to a mold. Eachspring 452 may have a stiffness that is determined based on theresistive force associated with removing the digital design of thealigner from a respective tooth that may have attachments, and ageometry of an undercut of an attachment on the teeth. The numericalsimulation may simulate removing the digital design of the aligner fromeach of the springs by applying one or more forces and/or displacementsto lift the digital design of the aligner from the springs. If the forcerequired to break the spring is more than a threshold amount of force,then the processing logic may determine a probable point of damage ispresent at a portion of the digital design of the aligner associatedwith that spring. It should be understood that the numerical simulationis calculated concurrently for every spring 452 while the digital designof the aligner is being removed.

FIG. 5A illustrates a flow diagram for a method 500 of performinganalysis on a digital design of an aligner (e.g., a polymeric aligner)using numerical simulation by modeling a subset of teeth and bondedattachments of a dental arch as springs, in accordance with oneembodiment. One or more operations of method 500 are performed byprocessing logic of a computing device. The processing logic may includehardware (e.g., circuitry, dedicated logic, programmable logic,microcode, etc.), software (e.g., instructions executed by a processingdevice), firmware, or a combination thereof. For example, one or moreoperations of method 500 may be performed by a processing deviceexecuting an aligner design analysis module 1450 of FIG. 14. It shouldbe noted that the method 500 may be performed for each unique alignerfor each patient's treatment plan, or for each unique aligner at keystages of the treatment plan. Further, method 500 includes operationsthat may be performed during block 104 of FIG. 1A.

At block 502, processing logic may perform the analysis on the digitaldesign of the aligner using numerical simulation associated with removalof the aligner from the dental arch-like structure. The numericalsimulation may include finite element analysis, finite element method,finite difference method, finite volume method, meshfree methods, smoothparticle galerkin method, or the like.

At block 504, processing logic may simulate one or more forces and/ordisplacements on the digital design of the aligner that are associatedwith removal of the aligner from the dental arch-like structure (e.g.,mold or the dental arch of the patient). Simulating the one or moreforces and/or displacements on the digital design of the aligner mayinclude performing operations at blocks 506, 508, and 510. At block 506,processing logic may model subsets of teeth of the dental arch of thepatient as subsets of springs. Each spring of the subsets of springs maybe attached to a respective cavity of the digital design of the aligner.It should be understood that not every tooth in the dental arch of thepatient is modeled as a spring in this embodiment. Each of the subset ofsprings may model at least one different tooth than another subset ofsprings. The subsets of springs are used in different numericalsimulations of removing the aligner from the dental arch-like structure.By only performing the numerical simulation using a subset of springs,less computations are concurrently performed and the numericalsimulation may perform faster than performing the numerical simulationon every spring modeling every tooth of the dental arch. The method 500may iterate through performing the numerical analysis on differentsubsets of springs until every spring has been involved in a numericalsimulation of removing the digital design of the aligner.

At block 508, processing logic may determine a force required to movethe aligner from another spring-connected tooth model (e.g., the modeldescribed with reference to the method 400 in FIG. 4A). At block 510,for each spring of a subset of springs in a simulation, processing logicmay perform operations at block 512 and 514. At block 512, processinglogic may determine the forces required to move the aligner from theanother spring-connected tooth model and apply that force on thealigner. At block 514, processing logic may determine if the alignerunder this load satisfies the damage criteria. The damage criteria mayrelate to a value of stress/strain or deformation energy exceeding athreshold value. In an embodiment, processing logic may determine that apoint on the digital design of the aligner is a probable point of damageresponsive to determining that the amount of force required to break thespring associated with the point exceeds the threshold amount of force.One or more corrective actions may be performed in response todetermining that there is a probable point of damage. In someembodiments, the digital design of the aligner may be input into thetrained machine learning model to verify the probable point of damage.

FIG. 5B illustrates an example numerical simulation 550 that models asubset of teeth of the dental arch of the patient as springs 552, inaccordance with one embodiment. As depicted, a subset of springs 552 areinserted into respective cavities of a digital design of the aligner 554just as a tooth would be when the aligner is worn or attached to a mold.Springs are not included in some of the cavities of the digital designof the aligner 554 in the depicted numerical simulation 550. Differentsubsets of springs may be modeled in different numerical simulationsuntil every modeled spring for every tooth is involved in a numericalsimulation of removing the digital design of the aligner 554. Eachspring 552 may have a stiffness that is determined based on theresistive force associated with removing the digital design of thealigner from a respective tooth that may have attachments, and ageometry of an undercut of an attachment on the teeth. The numericalsimulation may simulate removing the digital design of the aligner fromthe subset of springs by applying one or more forces to lift the digitaldesign of the polymeric aligner from the subset of springs. If a vale ofstress/strain or deformation energy at any point on the spring satisfiesa damage criteria by exceeding a threshold value, then the processinglogic may determine a probable point of damage is present at a portionof the digital design of the aligner associated with that first spring.It should be understood that the numerical simulation is calculatedconcurrently for every spring 552 in the subset of springs while thedigital design of the aligner is being removed.

FIG. 6A illustrates a flow diagram for a method 600 of performinganalysis on a digital design of an aligner (e.g., a polymeric aligner)using numerical simulation, in accordance with one embodiment. One ormore operations of method 600 are performed by processing logic of acomputing device. The processing logic may include hardware (e.g.,circuitry, dedicated logic, programmable logic, microcode, etc.),software (e.g., instructions executed by a processing device), firmware,or a combination thereof. For example, one or more operations of method600 may be performed by a processing device executing an aligner designanalysis module 1450 of FIG. 14. It should be noted that the method 600may be performed for each unique aligner for each patient's treatmentplan, or for each unique aligner at key stages of the treatment plan.Further, method 600 includes operations that may be performed duringblock 104 of FIG. 1A.

At block 602, processing logic may perform the analysis on the digitaldesign of the aligner using numerical simulation to determine an overallstrength of the aligner under one or more loading conditions. Thenumerical simulation may include finite element method, finitedifference method, finite volume method, meshfree methods,smoothed-particle methods, combinations of these methods, or the like.

At block 604, processing logic may gather one or more materialproperties (also referred to as material property information) of thealigner. The material properties may include an amount or value ofstress and/or strain that the material can sustain before cracking,breaking, deforming, warping, etc. One example of a material property ofthe material is the Young's Modulus of the material. In someembodiments, the material properties may not change between differentdigital designs of aligners because the aligners will be made of thesame material (e.g., polymeric). Material properties may be included ina configuration of the aligner design analysis module 1450 inembodiments.

At block 606, processing logic may gather a geometry of the aligner fromthe digital design of the aligner. The geometry may be specific to eachpatient (and to each stage of treatment) and may be determined based onthe dental arch of the patient. The geometry may be obtained bygenerating the digital design of the aligner by manipulating a digitalmodel of a dental arch-like structure (e.g., of a mold or dental arch ofa patient). The digital model of the dental arch-like structure mayrepresent the dental arch of the patient. The digital model of thedental arch-like structure may be offset to approximate a surface of thealigner and to generate the digital design of the aligner. As such, thedigital design of the aligner may include cavities configured to receiveteeth (referred to as tooth-receiving cavities or caps) of the patientand/or attachments on the teeth.

At block 607, processing logic may gather clinical information and/ortreatment-related information associated with the aligner (and with thedigital design of the aligner). The clinical information may include atleast one of tooth crowding information, tooth undercut information,tooth geometry information, tooth size, tooth shape, tooth numbers, ordistance between teeth, for example. The treatment-related informationmay include at least one of numbers of attachments associated with oneor more of the plurality of tooth receiving cavities, types ofattachments associated with one or more of the plurality of toothreceiving cavities, placement locations of attachments on teeth, orprecision cut information associated with one or more of theinterproximal regions. In some embodiments, such information is includedin a lookup table that may be referenced by processing logic and/or bythe simulation.

At block 608, processing logic may simulate one or more loads on thedigital design of the aligner (e.g., on the geometry of the digitaldesign of the aligner). The simulated loads may include one or more of abending load, a twisting load, a uniaxial tension load, a uniaxialcompression load, a shear load, and/or another load. The simulated loadmay be a simulated force, moment, or displacement (e.g., translationand/or rotation) in embodiments. Simulating the one or more loads on thedigital design of the aligner may include performing operations atblocks 610, 614, 616, and 618.

At block 610, processing logic may select a region of the digital designof the aligner, and may then proceed to perform the operations of blocks614-618 to test a strength associated with the selected the region. Atblock 610, each of a set of regions may be selected, and the operationsof blocks 614-618 may be repeated for each of the regions. The selectedregions may each be weak spots of the aligner, such as interproximalregions of the aligner.

FIG. 6F illustrates weak spots 655, 660, 665 of an aligner 626, inaccordance with one embodiment. The weak spots may correspond tointerproximal regions of the aligner.

Returning to FIG. 6A, at block 614, processing logic applies one or moreloading conditions around a selected region (e.g., around a weak spot orinterproximal region. As indicated above, the loading conditions mayinclude a bending load, a twisting load, a uniaxial tension load, auniaxial compression load, and/or a shear load, which may be appliedseparately or together. In one embodiment, the load is a moment orforce, such as a lifting force, a bending force, a twisting force, ashear force, a tension force, or a compression force. In such anembodiment in which a force or moment is applied, a strain and/or astrain energy may be computed. In one embodiment, the load is adisplacement (e.g., a translational displacement and/or a rotationaldisplacement), and a stress may be computed.

A loading condition around a region may be simulated by applying firstboundary conditions to one or more regions on a first side of the regionand by applying second boundary conditions to one or more additionalregions on a second side of the region. For example, a loading conditionaround an interproximal region may be simulated by fixing one or morefirst tooth-receiving cavities on a first side of the interproximalregion in place and applying a load to one or more secondtooth-receiving cavities on a second side of the interproximal region.In one embodiment, the load is applied to occlusal surfaces of the oneor more second tooth-receiving cavities.

Clinical information and/or treatment-related information may becorrelated with a magnitude of a load that needs to be applied to removea region of the aligner (e.g., a tooth-receiving cavity of the aligner)from an associated tooth-like structure. For example, the number ofattachments on one or more tooth-like structures that are adjacent to atooth-receiving cavity may affect a resistive force associated withremoving the aligner from the dental arch at the tooth-receiving cavity.To account for such interactions in the simulation, an amount of loadthat is applied around a region (e.g., around an interproximal region)may be based on the number of attachments associated with one or moreteeth that are adjacent to the region. Other clinical information and/ortreatment related information may also be used to adjust a magnitude ofthe load that is applied. Such information may include, for example, jawshape, tooth size, tooth shape, tooth numbers, tooth position,attachment types, attachment sizes, attachment numbers, etc.

FIG. 6B illustrates application of a bending load 634 around a region633 of an aligner 626, in accordance with one embodiment. The region 633may be an interproximal region connecting a first tooth-receiving cavity(cap) 628 and a second tooth-receiving cavity (cap) 635. The bendingload 634 may be applied about an axis 632 that runs through the region633. For example, the bending load 634 at interproximal region 633 maybe simulated by fixing first tooth-receiving cavity 628 and/or a thirdtooth-receiving cavity 627 on a first side of the interproximal region633 in place (e.g., by setting a 0 displacement boundary condition) andapplying a load to second tooth-receiving cavity 630 on a second side ofthe interproximal region 633 (e.g., by setting a force boundarycondition or a displacement boundary condition for the secondtooth-receiving cavity). In one embodiment, the load is applied totooth-receiving cavity 630, which may be a most terminal tooth-receivingcavity of the aligner 626. In another embodiment, the bending load 634is applied to tooth-receiving cavity 635, which is adjacent totooth-receiving cavity 628. In order to simulate application of a loadon a next interproximal region 629, the boundary conditions ontooth-receiving cavity 628 may be removed, and boundary conditions maybe set for tooth-receiving cavity 627. The load may then again beapplied to tooth-receiving cavity 630.

As mentioned, a magnitude of the load, which might include force,moment, torque, displacement, rotation and so on, that is applied todetermine a strain, stress and/or strain energy at a region (e.g., at aninterproximal region) may be based on clinical information and/ortreatment-related information. In one embodiment, the amount of load toapply around interproximal region 633 is based at least in part on anumber of attachments associated with tooth-receiving cavity 628 (e.g.,a number of attachments to be placed on a tooth that will mate withtooth-receiving cavity 628) and/or a number of attachments associatedwith tooth-receiving cavity 627. The presence of attachments on theteeth associated with these tooth-receiving cavities 627, 628 mayincrease an amount of force that is necessary to remove the aligner froma mold. Accordingly, the load that is simulated for the interproximalregion 633 may be increased an amount based on the number of attachmentsassociated with tooth-receiving cavity 627 and/or tooth-receiving cavity628. In one embodiment, a force of 1 Newton (N) is applied to simulateloading around interproximal region 633 if there are no attachmentsassociated with tooth-receiving cavity 627 and/or if there are noattachments associated with tooth-receiving cavity 628. In oneembodiment, for each attachment associated with tooth-receiving cavity627, a magnitude of the force applied is increased by one Newton, or byanother amount, to test the strain at interproximal region 633. In oneembodiment, for each attachment associated with tooth-receiving cavity628, a magnitude of the force is increased by one Newton, or by anotheramount, to test the strain at interproximal region 633.

FIG. 6C illustrates application of a twisting load 638 around a regionof aligner 626, in accordance with one embodiment. The region 633 may bean interproximal region connecting first tooth-receiving cavity (cap)628 and second tooth receiving cavity (cap) 635.The twisting load 638may be applied about an axis 636 that runs through the region 633. Forexample, the twisting load 638 at interproximal region 633 may besimulated by fixing first tooth-receiving cavity 628 and/or thirdtooth-receiving cavity 627 on a first side of the interproximal region633 in place (e.g., by setting a 0 displacement boundary condition) andapplying a load or displacement to second tooth-receiving cavity 630 ona second side of the interproximal region 633 (e.g., by setting a forceboundary condition or a displacement boundary condition for the secondtooth-receiving cavity). In one embodiment, the load is applied totooth-receiving cavity 630, which may be a most terminal tooth-receivingcavity of the aligner 626. In another embodiment, the twisting load 634is applied to tooth receiving cavity 635, which is adjacent totooth-receiving cavity 628.

FIG. 6D illustrates application of a uniaxis tension load 642 around aregion 633 of aligner 626, in accordance with one embodiment. The region633 may be an interproximal region connecting first tooth-receivingcavity (cap) 628 and second tooth receiving cavity (cap) 635.Theuniaxial tension load 642 may be applied along an axis that runs throughthe region 633. For example, the uniaxial tension load 642 atinterproximal region 633 may be simulated by fixing firsttooth-receiving cavity 628 and/or third tooth-receiving cavity 627 on afirst side of the interproximal region 633 in place (e.g., by setting a0 displacement boundary condition) and applying a load to secondtooth-receiving cavity 630 on a second side of the interproximal region633 (e.g., by setting a force boundary condition or a displacementboundary condition for the second tooth-receiving cavity). In oneembodiment, the load is applied to tooth-receiving cavity 630, which maybe a most terminal tooth-receiving cavity of the aligner 626. In anotherembodiment, the uniaxis tension load 642 is applied to tooth receivingcavity 635, which is adjacent to tooth-receiving cavity 628.

FIG. 6E illustrates application of a shear load 646 around a region 633of an aligner, in accordance with one embodiment. The region 633 may bean interproximal region connecting first tooth-receiving cavity (cap)628 and second tooth receiving cavity (cap) 635.In an example, the shearload 646 at interproximal region 633 may be simulated by fixing firsttooth-receiving cavity 628 and/or third tooth-receiving cavity 627 on afirst side of the interproximal region 633 in place (e.g., by setting a0 displacement boundary condition) and applying a load to secondtooth-receiving cavity 630 on a second side of the interproximal region633 (e.g., by setting a force boundary condition or a displacementboundary condition for the second tooth-receiving cavity). In oneembodiment, the load is applied to tooth-receiving cavity 630, which maybe a most terminal tooth-receiving cavity of the aligner 626. In anotherembodiment, the shear load 646 is applied to tooth receiving cavity 635,which is adjacent to tooth-receiving cavity 628.

Some loads that may be applied may include a combination of bending,twisting, lifting, shear, compression and/or tension in embodiments. Forexample, a load that is applied to one or more regions of the alignermay include a first magnitude along an x-axis (e.g., in a buccaldirection), a second magnitude along a y-axis (e.g., in a mesialdirection) and/or a third magnitude along a z-axis (e.g., in a verticaldirection). For example, a load may include a 0 N force along thex-axis, a 0.2 N force along the y-axis, and a 1 N force along thez-axis. The example load may additionally or alternatively includerotational forces about one or more of the x-axis, y-axis and/or z-axis.For example, the example load may include a force of 0 N about thex-axis, a force of 0.2-1.0 N about the y-axis, and a force of 0 N aboutthe z-axis.

Returning to FIG. 6A, at block 616, an amount of strain, stress and/orstrain energy (e.g., strain energy density) is determined for each ofthe simulated loading conditions using the numerical simulation. Theamount of strain, stress and/or stress energy may be determined based onthe loading conditions and the material property information.Additionally, one or more derived values may be derived from the strain,stress and/or strain energy density. The numerical simulation performedmay include solving a series of partial differential equations thatmodel applying one or more loads (e.g., forces and/or displacements) tothe aligner having the material properties and the geometry. Further,the partial differential equations may calculate a stress or strainvalue at the selected region (e.g., at the weak spot or interproximalregion). The partial differential equations may be elastostatic orelastodynamic partial differential equations that calculate stress,strain energy and/or strain states within the digital design of thealigner, which may be used to predict breakage, warpage, deformation,etc. In one embodiment, the amount of strain, stress and/or strainenergy is determined for an edge of the aligner at the region (e.g.,where the region interfaces with a outline of the aligner).

At block 618, processing logic calculates a strength value for theregion (e.g., weak spot or interproximal region) based on the determinedamount of strain, stress and/or strain energy (e.g., strain energydensity) for one or more of the simulated loads. The strength value mayadditionally or alternatively be based on one or more derived valuesthat are derived from at least one of the strain, the stress and/orstrain energy density. In one embodiment, the strength value for theregion is based on the strain, stress and/or strain energy densitycalculated for each of multiple different loading conditions. Forexample, the strength value for the region may be based on a maximumstrain, stress and/or strain energy density from the strains, stressesand/or strain energy density values computed for the region.

A determination may be made based on the strength value for the regionwhether the region is or includes a probable point of damage. Forexample, if the maximum calculated stress, strain and/or strain energydensity for the region exceeds a threshold, then the region may beidentified as a probable point of damage for the aligner.

At block 620, processing logic may determine a generalized strengthvalue of the whole aligner. The generalized strength value may be basedon the determined strength values of each of the tested regions. In oneembodiment, the strength value corresponds to a minimum strength valueof the tested regions.

At block 622, processing logic may determine whether the strength valuesatisfies a damage criterion or criteria. The damage criteria may besatisfied when the value of the stress and/or strain and/or strainenergy density exceeds a threshold value. The partial differentialequations may be used to calculate a strain/stress, strain energydensity and/or deformation energy value at each tested region.

At block 622, processing logic may determine that the aligner includesone or more probable point of damage responsive to determining that thestrength value satisfies the damage criteria (e.g., the value of localdeformation (strains and stresses) exceeds the threshold (e.g., 1-20%strain or 0.5-20 MPa stress)). If the strain and/or stress valuecalculated at the point that results from the force exceeds thethreshold, then a crack may initiate and breakage may result, thestrain/stress or deformation energy may cause warpage of the aligner,deformation of the aligner, or the like. The threshold that is definedfor the strain/stress, strain energy density and/or deformation energymay relate to yield criteria such as von Mises that the polymericmaterial will fail when the strain/stress or deformation energy valuereaches a critical value, or may be any suitable configurable threshold.

If the aligner has a generalized strength value that satisfies thedamage criteria (e.g., one or more regions of the aligner have a strain,stress and/or strain energy that exceeds a threshold), then it may bedetermined that the aligner includes one or more probable points ofdamage. Responsive to determining that the aligner includes one or moreprobable points of damage, processing logic may select for the aligner amanufacturing flow for aligners comprising one or more probable pointsof failure, such as described with reference to FIG. 1B. Alternatively,responsive to determining that the aligner includes one or more probablepoints of damage, processing logic may implement one or more correctiveactions as described above in order to generate a modified digital modelof the aligner. Some examples of modifying the digital model of thealigner include modifying a outline radius of the digital model of thealigner (e.g., at an interproximal region that is a probable point ofdamage), modifying a thickness of a portion of the digital model of thealigner (e.g., at an interproximal region that is a probable point ofdamage), modifying a geometry of the digital model of the aligner (e.g.,at or around an interproximal region that is a probable point ofdamage), and inserting an indicator in the digital model of the aligner,wherein the indicator represents a recommended place to begin removingthe aligner from a mold of the dental arch. In another example,processing logic may generate a modified digital model of a dental archby modifying one or more attachments on one or more teeth in the digitalmodel of the dental arch, and may then generate the modified digitalmodel of the aligner based on the modified digital model of the dentalarch. In another example, processing logic may generate a modifieddigital model of the dental arch by adding a new virtual filler orenlarging an existing virtual filler to a location on the digital modelof the dental arch that is associated with the interproximal region thatis the probable point of damage, and may then generate the modifieddigital model of the aligner based on the modified digital model of thedental arch.

FIG. 7A illustrates a flow diagram for a method 700 of performinganalysis on a digital design of an aligner (e.g., a polymeric aligner)using a geometrical evaluator, in accordance with one embodiment. Thegeometrical evaluator may be considered as one type of numericalsimulation in embodiments. One or more operations of method 700 areperformed by processing logic of a computing device. The processinglogic may include hardware (e.g., circuitry, dedicated logic,programmable logic, microcode, etc.), software (e.g., instructionsexecuted by a processing device), firmware, or a combination thereof.For example, one or more operations of method 700 may be performed by aprocessing device executing an aligner design analysis module 1450 ofFIG. 14. It should be noted that the method 700 may be performed foreach unique aligner for each patient's treatment plan, or for eachunique aligner at key stages of the treatment plan. Further, method 600includes operations that may be performed during block 104 of FIG. 1A.

At block 702, processing logic may perform the analysis on the digitaldesign of the aligner using a geometrical evaluator (e.g., a numericalsimulation) to determine an overall strength of the aligner. Thegeometrical evaluator may determine one or more geometrical propertiesof the digital design of the aligner at one or more regions of thealigner (e.g., at one or more interproximal regions and/or other weakspots of the digital design of the aligner), and may compute a stress orstiffness, or strength based on the one or more geometrical propertiesand material properties of a material to be used to manufacture thealigner in embodiments.

At block 704, processing logic may gather one or more materialproperties (also referred to as material property information) of thealigner. The material properties may include an amount or value ofstress and/or strain that the material can sustain before cracking,breaking, deforming, warping, etc. One example of a material property ofthe material is the Young's Modulus of the material. In someembodiments, the material properties may not change between differentdigital designs of aligners because the aligners will be made of thesame material (e.g., polymeric). Material properties may be included ina configuration of the aligner design analysis module 1450 inembodiments.

At block 706, processing logic may gather a geometry of the aligner fromthe digital design of the aligner. The geometry may be specific to eachpatient (and to each stage of treatment) and may be determined based onthe dental arch of the patient. The geometry may be obtained bygenerating the digital design of the aligner by manipulating a digitalmodel of a dental arch-like structure (e.g., of a mold or dental arch ofa patient). The digital model of the dental arch-like structure mayrepresent the dental arch of the patient. The digital model of thedental arch-like structure may be offset to approximate a surface of thealigner and to generate the digital design of the aligner. As such, thedigital design of the aligner may include cavities configured to receiveteeth (referred to as tooth-receiving cavities or caps) of the patientand/or attachments on the teeth.

At block 707, processing logic may determine locations of the potentialweak spots such as interproximal regions of the aligner. It is to notethat the potential weak spots usually appear at interproximal regionsdue to weak connection. However, it can exist in other spots as indifferent dentitions. In one embodiment, the locations of theinterproximal regions are determined by first determining centers of thetooth-receiving cavities of the aligner. Lines may then be computedbetween the centers of each pair of adjacent tooth-receiving cavities.For each pair of adjacent tooth-receiving cavities, a midpoint of theline drawn between the centers of the tooth-receiving cavities may be amidpoint of the interproximal region connecting those twotooth-receiving cavities. The interproximal region connecting the twoadjacent tooth-receiving cavities may include the area around themidpoint of the line (e.g., from a first offset in a first directionalong the line from the midpoint to a second offset in a seconddirection along the line from the midpoint).

At block 708, processing logic may analyze the determined potential weakspots (e.g., interproximal regions) of the aligner. Analysis of thepotential weak spots may include computing geometrical values of thepotential weak spots (e.g., area moments of inertia) and/or computingstresses based on one or more loads applied to the potential weak spots.Analyzing the potential weak spots of the aligner may include performingoperations at blocks 710, 712, 714, 716, and 718.

At block 710, processing logic may select a potential weak spot (e.g.,an interproximal region) of the digital design of the aligner, and maythen proceed to perform the operations of blocks 712-718 to test astrength associated with the selected potential weak spot. At block 710,each of a set of potential weak spots may be selected, and theoperations of blocks 712-718 may be repeated for each of the potentialweak spots. The selected potential weak spots may be interproximalregions of the aligner in some embodiments.

FIG. 7B illustrates an aligner 724 including teeth-receiving cavitiesand interproximal regions 730A-M between pairs of teeth-receivingcavities, in accordance with one embodiment. The location of eachinterproximal region 730A-M may have been determined as set forth above.For example, a center of a first tooth-receiving cavity 726 and a centerof a second tooth-receiving cavity 728 may be determined. A line 732 maythen be drawn between the center of the first tooth-receiving cavity 726and the center of the second tooth-receiving cavity 728. Theinterproximal region 730D may then be determined to be at approximatelythe midpoint of the line 732. The other interproximal region locationsmay be similarly determined.

Returning to FIG. 7A, at block 712, processing logic determines one ormore cross-sectional slices for a selected potential weak spot. In oneembodiment, one or more of the cross-sectional slices are through themidpoint of the potential weak spot (e.g., through the midpoint of aninterproximal region). Additional cross-sectional slices may then betaken at locations that are offset from the midpoint along the line. Inone embodiment, 5, 10, 15 or 20 cross-sectional slices are generated.Alternatively, other numbers of cross-sectional slices may be generated.

Each cross sectional slice may define a plane comprising a first axisand a second axis. The first axis for each plane may be perpendicular tothe line drawn between the centers of the tooth-receiving cavities thatthe interproximal region in question separates, and may further beperpendicular to a z-axis (where the z-axis is a vertical axis and/or anaxis that is normal to an occlusal plane defined by the aligner). Asecond axis of the planes defined by the cross-sectional slices may bethe z-axis. Alternatively, a second axis of the plane for one or moreplanes defined by cross-sectional slices may be at an angle to thez-axis. In order to determine a cross-sectional slice, processing logicmay determine an additional line that is perpendicular to the lineconnecting the centers of the tooth-receiving cavities and that isperpendicular to the z-axis. A plane may then be determined having afirst axis defined by the additional line and having a second axis thatis parallel to the z-axis or that is at an angle to the z-axis. Thedigital model of the aligner may then be sliced by the plane, generatinga cross-sectional slice.

FIG. 7C illustrates a cross-sectional slice 740 taken of an aligner 734,in accordance with one embodiment. The cross-sectional slice 740 istaken at an interproximal region of the aligner 734 by slicing throughthe aligner at a plane 736 defined by a first axis 738 and a second axis737.

Returning to FIG. 7A, at block 714, for each determined cross-sectionalslice, one or more strength values are calculated. Such values may bebased, for example, on a stress, a strain, a strain energy, or one ormore derived values that are derived from the stress, strain and/orstrain energy. In one embodiment, one or more area moments of inertiaare computed for each slice. The area moment of inertia of across-section of aligner is computed separately for each axis ofinterest. For example, the area moment of inertia of a cross-section maybe determined with reference to the first axis of the plane defined bythe cross-sectional slice (e.g., x-axis or buccal-lingual axis), withreference to the second axis of the plane defined by the cross-sectionalslice (e.g., z-axis or occlusal normal axis), with reference to a thirdaxis that is normal to the plane defined by the cross-sectional slice(e.g., y-axis), and/or with reference to a line on the plane defined bythe cross-sectional slice (e.g., the line defined by the equation x=z).The area moment of inertia of a cross sectional slice of the alignerrelated to an axis may be calculated by:

$I = {\underset{R}{\int\int}x^{2}{dA}}$

Where I is the area moment of inertia, where x is the perpendiculardistance from the axis to the element dA, where dA is an elemental area,and where R is an arbitrary shape.

For each area moment of inertia I, one or more stress values σ may thenbe determined. A stress σ associated with the area moment of inertia maybe computed by:

$\sigma = \frac{M*d}{I}$

Where d is the distance to the axis from a point on the aligner, andwhere M is a moment or force applied at the point.

A maximum stress σ_(max) may be computed for each area moment of inertiaby:

$\sigma_{m\; {ax}} = \frac{M*d_{m\; {ax}}}{I}$

where d_(max) is the largest distance to the axis from any point on thealigner. In some embodiments, the material properties of the material tobe used to manufacture the aligner may also be used in the computationof the stress and the maximum stress.

FIG. 7D illustrates a bending load 742 applied around a first axis 738of the cross-sectional slice 740 of FIG. 7C, in accordance with oneembodiment. As shown, the area moment of inertia is computed for thecross-sectional slice 740 at the first axis 738. A bending force ormoment about the axis 738 is then computed using the area moment ofinertia at the first axis 738.

FIG. 7E illustrates a bending load 744 applied around a second axis 737(e.g., of the cross-sectional slice 740 of FIG. 7C, in accordance withone embodiment. As shown, the area moment of inertia is computed for thecross-sectional slice 740 at the second axis 737. A bending force ormoment about the axis 737 is then computed using the area moment ofinertia at the second axis 737.

FIG. 7F illustrates a torsion load 746 applied around a third axis 748normal to the cross-sectional slice 740 of FIG. 7C, in accordance withone embodiment. As shown, the area moment of inertia is computed for thecross-sectional slice 740 at the third axis 748. A torsion force ormoment about the axis 748 is then computed using the area moment ofinertia at the third axis 748.

Returning to FIG. 7A, at block 716, processing logic calculates aminimum strength value for the potential weak spot. In one embodiment,the minimum strength value is computed based on the minimum area momentof inertia and/or the maximum stress computed for the potential weakspot. As noted, multiple cross-sectional slices are generated for thepotential weak spot, and multiple area moments of inertia are computedfor each cross-sectional slice. Additionally, a maximum stress value maybe determined for each area moment of inertia. A minimum area moment ofinertia and/or a maximum stress may be determined from the multiple areamoments of inertia and/or multiple stress values that are computed for apotential weak spot. The minimum strength value may be, or may be basedon, the minimum area moment of inertia and/or the maximum stresscomputed for the potential weak spot. In one embodiment, a minimumstrength value and/or a maximum stress value is selected for each of thetypes of area moments of inertia that are computed. Accordingly, if fourdifferent area moments of inertia are computed, then the minimumstrength value may be based on a combination of four different minimumarea moments of inertia (e.g., for 4 different axes) and/or on acombination for four different maximum stresses (e.g., for the 4different axes).

At block 718, processing logic may determine whether the minimumstrength value for the potential weak spot (e.g., interproximal region)satisfies one or more damage criteria. The damage criteria may include astress threshold and/or an area moment of inertia threshold. If theminimum area moment of inertia is below an area moment of inertiathreshold and/or if the maximum stress is at or above the stressthreshold, then the damage criteria may be satisfied. Processing logicmay determine that the potential weak spot is a probable point of damageif the damage criteria are satisfied.

At block 720, processing logic may determine a generalized strengthvalue of the whole aligner. The generalized strength value may be basedon the determined strength values of each of the tested potential weakspots. In one embodiment, the strength value corresponds to a minimumstrength value of the tested interproximal regions.

At block 722, processing logic may determine whether the strength valuesatisfies a damage criterion or criteria. The damage criteria may besatisfied when the maximum stress value for any potential weak spotexceeds a stress threshold value and/or when the minimum area moment ofinertia for any potential weak spot is below an area moment of inertiathreshold.

If the aligner has a generalized strength value that satisfies thedamage criteria, then it may be determined that the aligner includes oneor more probable points of damage. Responsive to determining that thealigner includes one or more probable points of damage, processing logicmay select for the aligner a manufacturing flow for aligners comprisingone or more probable points of failure, such as described with referenceto FIG. 1B. Alternatively, responsive to determining that the alignerincludes one or more probable points of damage, processing logic mayimplement one or more corrective actions as described above in order togenerate a modified digital model of the aligner. Some examples ofmodifying the digital model of the aligner include modifying a outlineradius of the digital model of the aligner (e.g., at an interproximalregion that is a probable point of damage), modifying a thickness of aportion of the digital model of the aligner (e.g., at an interproximalregion that is a probable point of damage), modifying a geometry of thedigital model of the aligner (e.g., at or around an interproximal regionthat is a probable point of damage), and inserting an indicator in thedigital model of the aligner, wherein the indicator represents arecommended place to begin removing the aligner from a mold of thedental arch. In another example, processing logic may generate amodified digital model of a dental arch by modifying one or moreattachments on one or more teeth in the digital model of the dentalarch, and may then generate the modified digital model of the alignerbased on the modified digital model of the dental arch. In anotherexample, processing logic may generate a modified digital model of thedental arch by adding a new virtual filler or enlarging an existingvirtual filler to a location on the digital model of the dental archthat is associated with the interproximal region that is the probablepoint of damage, and may then generate the modified digital model of thealigner based on the modified digital model of the dental arch.

The metrics used in method 700 can either be used directly to predictthe probability of aligner/retainer breakage (as discussed above), orcan be used as features for training the machine learning model. Forexample, the area moments of inertia and/or the strain values determinedfor each of the interproximal regions may be used as inputs to train amachine learning model to predict probable points of damage, asdiscussed herein above. These metrics may be used along with, or insteadof, the metrics previously discussed with reference to training of themachine learning model. For example, embeddings in a training datasetmay each include a collection of area moments of inertia and/or strainvalues associated with one or more interproximal regions of an aligner,and may include a label indicating whether the aligner experienced apoint of damage and/or indicating a location of the point of damage(e.g., a particular interproximal region that was damaged).

FIG. 7G illustrates a superimposition 750 of three different alignersfor a dental arch, wherein each of the aligners is associated with adifferent stage of treatment of the dental arch, in accordance with oneembodiment. A first cross-section 752 of a first aligner associated witha first stage of treatment has a relatively wide base and short peak. Incomparison, a second cross-section 754 of a second aligner associatedwith a thirteenth stage of treatment has a narrower base and a tallerpeak. In further comparison, a third cross-section 756 of a thirdaligner associated with a twenty sixth stage of treatment has an evennarrower base and an even taller peak. Analyses of the three differentcross sections would yield a highest area moment of inertia and a loweststress for the first cross-section 752 and a lowest area moment ofinertia and a highest stress for the third cross-section 756.Accordingly, the third aligner may be identified as comprising aprobable point of damage and the first aligner may be identified as notcomprising a probable point of damage in an example.

There are multiple different loads that are applied on an aligner duringits lifetime. Such loads include those caused by a one-time removal ofthe aligner from a mold used to form the aligner, those caused byinsertion and removal of the aligner from a patient's dental arch, andthose caused by chewing and/or grinding a patient's teeth together whilean aligner is worn and those caused by handling and shipping. Forexample, during the removal process of the aligner from the mold, somedamage (e.g., permanent deformation or strain) may or may not occur toone or more points on the aligner. During intended use, a patient mayinsert and remove the aligner a few times a day for certain days fromone day to 3 weeks. Also, even if it is not recommended for patients towear aligners while eating, they may still do so. Additionally, whilewearing aligners patients may grind their teeth. Each of theaforementioned loads may cause some small amount of damage to thealigner depending on their intensity and amount of occurrence.Initiation and evolution of damage in a point/region might eventuallylead to crack initiation and propagation and eventually completefailure/breakage. To predict if a certain aligner design might break orto optimize the shape of the aligner to reduce probability of damageand/or failure, method 800 of FIG. 8A may be performed.

FIG. 8A illustrates a flow diagram for a method 800 of performinganalysis on a digital design of an aligner (e.g., a polymeric aligner)using numerical simulation that simulates a sequence of loads on thealigner, in accordance with one embodiment. One or more operations ofmethod 800 are performed by processing logic of a computing device. Theprocessing logic may include hardware (e.g., circuitry, dedicated logic,programmable logic, microcode, etc.), software (e.g., instructionsexecuted by a processing device), firmware, or a combination thereof.For example, one or more operations of method 800 may be performed by aprocessing device executing an aligner design analysis module 1450 ofFIG. 14. It should be noted that the method 800 may be performed foreach unique aligner for each patient's treatment plan, or for eachunique aligner at key stages of the treatment plan. Further, method 800includes operations that may be performed during block 104 of FIG. 1A.Method 800 may simulate sequential loadings and any associated causeddamage from initial manufacture to final use of an aligner. Such asimulation allows processing logic to predict damage initiation, damageevolution, and/or failure/breakage.

At block 802, processing logic may perform the analysis on the digitaldesign of the aligner using numerical simulation. The numericalsimulation may include finite element method, finite difference method,finite volume method, meshfree methods, smoothed-particle methods,combinations of these methods, or the like.

At block 804, processing logic may gather one or more materialproperties (also referred to as material property information) of thealigner. The material properties may include an amount or value ofstress and/or strain that the material can sustain before cracking,breaking, deforming, warping, etc. for example elastic modulus, Poissonratio, yield strength, strain-stress curve, etc. In one embodiment, thematerial properties include an undamaged response curve and/or aprogressive damage curve associated with the material. Materialproperties may be included in a configuration of the aligner designanalysis module 1450 in embodiments.

At block 806, processing logic may gather a first geometry of thealigner from the digital design of the aligner. In embodiments, this mayinclude gathering the digital design of the aligner. The first geometrymay be specific to each patient (and to each stage of treatment) and maybe determined based on the dental arch of the patient. The firstgeometry may be obtained by generating the digital design of the alignerby manipulating a digital model of a dental arch-like structure (e.g.,of a mold or dental arch of a patient). The digital model of the dentalarch-like structure may represent the dental arch of the patient. Thedigital model of the dental arch-like structure may be offset toapproximate a surface of the aligner and to generate the digital designof the aligner. As such, the digital design of the aligner may includecavities configured to receive teeth (referred to as tooth-receivingcavities or caps) of the patient and/or attachments on the teeth.

At block 808, processing logic may gather a second geometry of thedental arch-like structure from a digital model of the dental arch-likestructure (e.g., mold). In embodiments, this may include gathering thedigital model of the dental arch-like structure. The digital model ofthe dental arch-like structure may be generated from informationobtained by performing an intraoral scan of the patient during aconsultation and/or from a treatment plan. For example, the dental archof the patient may be digitized, via scanning, and modeled as the dentalarch used to fabricate the mold. The second geometry may includeinformation related to the dental arch of the patient, such as the toothsize, tooth shape, tooth orientation, distance between teeth,attachments on teeth, upper dental arch, lower dental arch, etc. Thedental arch-like structure may represent an upper dental arch or a lowerdental arch of a patient at a stage of treatment.

At block 808, processing logic may additionally gather a third geometryof an opposing dental arch-like structure from a digital model of theopposing dental arch-like structure (e.g., mold). In embodiments, thismay include gathering the digital model of the opposing dental arch-likestructure. The digital model of the opposing dental arch-like structuremay be generated from information obtained by performing an intraoralscan of the patient during a consultation and/or from a treatment plan.The third geometry may include information related to the opposingdental arch of the patient, such as the tooth size, tooth shape, toothorientation, distance between teeth, attachments on teeth, upper dentalarch, lower dental arch, etc. The opposing dental arch-like structuremay represent an upper dental arch or a lower dental arch of a patientat a stage of treatment.

At block 809, processing logic may simulate progressive damage to thealigner to determine a total amount of damage to each of one or moreregions of the aligner. Processing logic may simulate a sequence of oneor more forces and/or displacements on the digital design of the alignerthat are associated with removal of the aligner from the dentalarch-like structure (e.g., mold or the dental arch of the patient),placement of the aligner on the dental arch-like structure, chewing, andso on. Simulating the one or more forces and/or displacements on thedigital design of the aligner may include performing operations atblocks 810, 812, 814, 816, and 818.

At block 810, processing logic may simulate a load on the aligner. Theload that is simulated may be any of the loads that have been previouslydiscussed (e.g., with reference to FIGS. 3A-7G). Additionally, the loadmay be simulated using any of the techniques and/or numericalsimulations that were previously discussed (e.g., with reference toFIGS. 3A-7G). In one embodiment, the simulated load simulates theremoval of the aligner having the one or more material properties andthe first geometry from the dental arch-like structure having the secondgeometry by applying the one or more loads (e.g., one or more forcesand/or displacements) to a set of points on the digital design of thealigner (e.g., as discussed with reference to FIGS. 3A-3B, FIGS. 4A-4B,FIGS. 5A-5B, or FIGS. 6A-6F). In one embodiment, the simulated loadsimulates placement of the aligner on the dental arch-like structure.Such a simulation of a load may be performed, for example, using aninverse of the forces that are applied to remove the aligner from thedental arch-like structure. In one embodiment, the simulated loadsimulates chewing forces on the aligner, which is discussed in greaterdetail below with reference to FIG. 8C. In embodiments, the load that isapplied includes one or more forces or moments.

At block 812, processing logic determines an amount of damage to each ofthe one or more regions of the aligner. This may include determiningamounts of damage for every region and/or point of the aligner. Damageto regions/points may be determined by first determining an amount ofstrain at each region/point as discussed above (e.g., with reference toFIGS. 3A-6F). The points on the aligner may be able to endure up to athreshold amount of strain without incurring damage or becomingpermanently deformed. However, strain at a point that exceeds thethreshold amount of strain may cause damage to the point on the aligner.Accordingly, the measured strain at a point/region of the aligner may bedivided into elastic strain and plastic strain. Elastic strain may betemporary strain that is reduced to 0 after force is no longer appliedto the aligner. Plastic strain may be permanent strain that may cause apermanent deformation of the aligner. Any amount of plastic strain at apoint/region of the aligner may result in an amount of damage to thealigner at that point/region. The amount of damage may be based on amagnitude of the plastic strain. In one embodiment, the amount of damagehas a value of 0 to 1, wherein 0 indicates no damage and 1 indicatesbreakage. The 0 damage value may represent 0% damage, and the 1 damagevalue may represent 100% damage.

At block 814, processing logic may update the digital model of thealigner based on the amounts of damage (e.g., amounts of plastic strain)at the respective points on the aligner. For each point/region on thealigner, an amount of damage may be recorded. This may be referred to asa damage initiation value applied to the point. Ideally, most or allregions/points on the aligner will have zero damage. The digital modelmay be updated so that a subsequent simulation of another load on thealigner will be applied to a modified digital model of the aligner,where any damage (e.g., plastic strain) that has already occurred isaccounted for in a starting condition of the aligner as included in themodified digital model of the aligner. Additionally, the digital modelmay be updated by adjusting a geometry of the digital model to accountfor the plastic strain and reflect any permanent deformation of thealigner associated with the plastic strain.

At block 816, processing logic determines whether any further loads onthe aligner are to be simulated. If no additional load on the aligner isto be simulated, the method continues to block 818, and processing logicstops simulating loads on the aligner. If a further load on the aligneris to be simulated, then the method returns to block 810, and anotherload on the aligner is simulated. In embodiments, a sequence of manydifferent loads may be simulated on the aligner. With each simulation,an amount of damage due to the simulated load may be used to update thedigital model of the aligner. This may cause plastic strain toaccumulate at certain points of the aligner, which may ultimately leadto those points of the aligner becoming broken or deformed to amagnitude that the aligner no longer serves its intended purpose. In oneembodiment, the sequence of simulations of loads on the alignerincludes:

1) a simulation of a one-time removal of the aligner from a mold of thedental arch used to form the aligner;

2) repeated simulations of removal of the aligner from the dental archof the patient and insertion of the aligner onto the dental arch of thepatient (e.g., between 10-200 successive simulations of removal andinsertion of the aligner); and/or 3) repeated simulations of chewingloads on the aligner.

Different simulation techniques described herein may be used insequence. For example, the techniques described with reference to FIGS.3A-3B may be used initially to simulate removal of the aligner from themold of the dental arch, and the techniques described with reference toFIGS. 4A-4B or FIGS. 6A-6F may subsequently be used to simulateapplication of the aligner onto the dental arch of the patient and/orremoval of the aligner from the dental arch of the patient.

At block 820, processing logic determines whether a damage criterion issatisfied for at least one region/point of the aligner based on thetotal amount of damage to each of the one or more regions. In oneembodiment, the damage criterion is a total amount of accumulatedstrain. In one embodiment, the damage criterion is 0 damage (e.g., anyamount of damage to any point on the aligner causes the aligner tosatisfy the damage criterion). In one embodiment, the damage criterionis 2% damage, 5% damage, 10% damage, 15% damage or 20% damage. If thedamage criterion is satisfied, then processing logic may initiate one ormore corrective actions and/or may select a specific manufacturing flowfor the aligner that is associated with aligners with probable points ofdamage, as discussed in detail earlier in this application.

In some embodiments, the operations of block 820 may be performed aftereach load is simulated on the aligner. If at any point a damagecriterion is satisfied for the aligner, then further simulation on thealigner may not be performed. This may enable processing logic to tracka damage evolution path of the aligner and determine at what pointduring the aligner's life it might fail as well as which of the loadingsis most detrimental to the aligner.

FIG. 8B illustrates a stress/strain curve 822 for an aligner, inaccordance with one embodiment. Stress (a) may represent force andstrain (c) may represent displacement. The stress/strain curve 822 mayinclude an undamaged response curve 824 (between points A, B, D and J)as well as a damage response curve (also referred to as a progressivedamage curve) 826 (between points D and F). As force is applied to apoint of the aligner, stress increases and the strain also increasesaccording to the undamaged response curve 824 up until the amount ofstrain reaches an amount sufficient to cause damage initiation (labeledD on the stress/strain curve 822). Between point A and point B, thestrain increases linearly with increases in stress according to materialproperties of the aligner at a rate associated with an elastic modulusor Young's modulus (E) (which is also the slope of the line of thestrain stress curve between points A and B). If an amount of strain isequal to or less than the strain at point B, then after a load thatcauses the strain is removed from the aligner, the strain returns topoint A (zero strain). The region between points A and B is called theplastic region, and any strain between point A and point B is elasticstrain.

When the strain exceeds point B, the slope changes according to theundamaged response curve 824 up until the strain reaches the damageinitiation value at point D. Any strain beyond point B representsplastic strain. Accordingly, the region between points B and D is theplastic region. If the strain is between point B and point D (e.g., atpoint C), then when the stress is no longer applied to the aligner thestrain reduces to a non-zero strain based on the elastic modulus orYoung's modulus € (and the initial slope). In the illustrated example,after a stress causes a strain that reaches point C is no longerapplied, the strain reduces to point H, which then represents theplastic strain or permanent deformation at the point of the aligner. Iffurther stress is then applied, the strain increases from point H topoint C, and then continues along the undamaged response curve 824 asstrain increases up to point D.

The portion of the undamaged response curve 824 between points D and Jrepresent what the curve would look like if no damage were to occur.However, past point D damage occurs to the aligner, which follows thedamage response curve 826 between points D and F. Any strain that ispast point D will cause the material properties of the aligner materialto change at the damaged point, which includes a lowered elasticity atthat point. This is reflected in a less steep slope for the strainstress response.

In the illustrated example the strain is shown to increase to point I.Once the load is no longer applied and the stress reduces to zero, thestrain reduces from point I to point G according to a new slope. The newslope may be computed according to the equation:

S=(1−d)E

Where S is the new slope for the strain stress curve, d is an amount ofdamage (from 0 to 1), and E is the elastic modulus. This reflects adegradation of the elasticity of the aligner material at the point thatis damaged. If further stress is applied, strain would then increasefrom point G until point I is reached according to the new slope S.Further increase in the strain would cause the strain to continue tofollow the damage response curve 826. If the strain ever reaches pointF, then the aligner breaks or cracks at the point.

FIG. 8C illustrates a flow diagram for a method 830 of performinganalysis on a digital design of an aligner (e.g., a polymeric aligner)using numerical simulation associated with chewing and/or grinding ofteeth, in accordance with one embodiment. One or more operations ofmethod 830 are performed by processing logic of a computing device. Theprocessing logic may include hardware (e.g., circuitry, dedicated logic,programmable logic, microcode, etc.), software (e.g., instructionsexecuted by a processing device), firmware, or a combination thereof.For example, one or more operations of method 830 may be performed by aprocessing device executing an aligner design analysis module 1450 ofFIG. 14. It should be noted that the method 830 may be performed foreach unique aligner for each patient's treatment plan, or for eachunique aligner at key stages of the treatment plan. Further, method 830includes operations that may be performed during block 104 of FIG. 1A.

At block 832, processing logic may perform the analysis on the digitaldesign of the aligner using numerical simulation associated with chewingand/or tooth grinding. The numerical simulation may include finiteelement method, finite difference method, finite volume method, meshfreemethods, smoothed-particle methods, combinations of these methods, orthe like.

At block 834, processing logic may gather one or more materialproperties (also referred to as material property information) of thealigner. The material properties may include an amount or value ofstress and/or strain that the material can sustain before cracking,breaking, deforming, warping, etc. One example of a material property ofthe material is the Young's Modulus of the material. In someembodiments, the material properties may not change between differentdigital designs of aligners because the aligners will be made of thesame material (e.g., polymeric).

At block 836, processing logic may gather a first geometry of thealigner from the digital design of the aligner. In embodiments, this mayinclude gathering the digital design of the aligner. The first geometrymay be specific to each patient (and to each stage of treatment) and maybe determined based on the dental arch of the patient. The firstgeometry may be obtained by generating the digital design of the alignerby manipulating a digital model of a dental arch-like structure (e.g.,of a mold or dental arch of a patient). The digital model of the dentalarch-like structure may represent the dental arch of the patient. Thedigital model of the dental arch-like structure may be offset toapproximate a surface of the aligner and to generate the digital designof the aligner. As such, the digital design of the aligner may includecavities configured to receive teeth (referred to as tooth-receivingcavities or caps) of the patient and/or attachments on the teeth.

At block 838, processing logic may gather a second geometry of thedental arch-like structure from a digital model of the dental arch-likestructure (e.g., mold). In embodiments, this may include gathering thedigital model of the dental arch-like structure. The digital model ofthe dental arch-like structure may be generated from informationobtained by performing an intraoral scan of the patient during aconsultation and/or from a treatment plan. For example, the dental archof the patient may be digitized, via scanning, and modeled as the dentalarch used to fabricate the mold. The second geometry may includeinformation related to the dental arch of the patient, such as the toothsize, tooth shape, tooth orientation, distance between teeth,attachments on teeth, upper dental arch, lower dental arch, etc. Thedental arch-like structure may represent an upper dental arch or a lowerdental arch of a patient at a stage of treatment.

At block 840, processing logic may additionally gather a third geometryof an opposing dental arch-like structure from a digital model of theopposing dental arch-like structure (e.g., mold). In embodiments, thismay include gathering the digital model of the opposing dental arch-likestructure. The digital model of the opposing dental arch-like structuremay be generated from information obtained by performing an intraoralscan of the patient during a consultation and/or from a treatment plan.The third geometry may include information related to the opposingdental arch of the patient, such as the tooth size, tooth shape, toothorientation, distance between teeth, attachments on teeth, upper dentalarch, lower dental arch, etc. The opposing dental arch-like structuremay represent an upper dental arch or a lower dental arch of a patientat a stage of treatment.

At block 842, processing logic may apply boundary conditions associatedwith a chewing load (or a tooth grinding load) to both the upper andlower dental arch of the patient (e.g., to the second geometry of thedigital model of the dental arch-like structure and to the thirdgeometry of the digital model of the opposing dental arch-likestructure). In an embodiment, the boundary conditions for the upperdental arch is a fixed position (e.g., zero displacement), and theboundary conditions for the lower dental arch is application of a load(e.g., a force) to one or more points on the lower dental arch. Inanother embodiment, the boundary conditions for the lower dental arch isa fixed position (zero displacement) and the boundary conditions for theupper dental arch is application of a load to one or more points on theupper dental arch. These applied boundary conditions may simulatecompression of the aligner between the upper dental arch and the lowerdental arch. In embodiments, approximately 0-2000 Newtons of force maybe applied to one dental arch in the direction of the opposing dentalarch. Depending on the shape of the teeth, the size of the teeth, theheights of the teeth, patient gender, patient age, and so on,compressive forces, and thus strain, may be distributed unevenly acrossthe various points of the aligner.

At block 844, processing logic may measure a strain on the variousregions or points of the aligner. The strain may then be used to assesswhether any points on the aligner are probable points of damage.

FIG. 9 illustrates a flow diagram for a method 900 for implementing oneor more corrective actions to an aligner (e.g., a polymeric aligner)based on a result one or more loads on the aligner. One or moreoperations of method 900 are performed by processing logic of acomputing device. The processing logic may include hardware (e.g.,circuitry, dedicated logic, programmable logic, microcode, etc.),software (e.g., instructions executed by a processing device), firmware,or a combination thereof. For example, one or more operations of method900 may be performed by a processing device executing an aligner designanalysis module 1450 of FIG. 14. It should be noted that the method 900may be performed for each unique aligner for each patient's treatmentplan, or for each unique aligner at key stages of the treatment plan.Further, method 900 includes operations that may be performed duringblock 104 of FIG. 1A.

At block 902, processing logic may simulate a load on the aligner usingany of the techniques set forth herein above. For example, processinglogic may simulate a removal of a polymeric aligner from a dental-archlike structure (e.g., mold or dental arch of a patient) using a firstdigital model and a second digital model. The first digital modelrepresents a digital arch-like structure of a patient and the seconddigital model represents a polymeric aligner to be supported by thedental arch-like structure and specifies one or more physical propertiesof the polymeric aligner at one or more regions of the polymericaligner.

At block 904, processing logic may determine a likeliness that one ormore values at the one or more regions will satisfy one or more damagecriteria. The values may represent a strain and/or stress or any otherquantities derived from those quantities determined at the one or moreregions during the simulated load on the aligner (e.g., during thesimulated removal of the polymeric aligner from the dental arch usingthe first digital model and the second digital model). The damagecriteria may be satisfied when the one or more values exceed a thresholdvalue. The threshold value may have been determined based on a trainedmachine learning model based on breakage data, in one embodiment. Thedetermination at block 904 may be based on an interaction of the dentalarch-like structure and the one or more physical properties of thepolymeric aligner, and the interaction being due to the simulatedremoval, in one embodiment.

At block 906, in response to analyzing the digital model of the alignerfor one or more likely points of physical damage based on thedetermination of the likeliness of the one or more values satisfying theone or more damage criteria, processing logic may determine whether toimplement one or more corrective actions for the aligner. If adetermination is made to implement one or more corrective actions,processing logic may implement the one or more corrective actions on thealigner.

FIG. 10 illustrates a flow diagram for a method 1000 of performinganalysis on a digital design of an aligner (e.g., a polymeric aligner)using a rules engine, in accordance with one embodiment. One or moreoperations of method 1000 are performed by processing logic of acomputing device. The processing logic may include hardware (e.g.,circuitry, dedicated logic, programmable logic, microcode, etc.),software (e.g., instructions executed by a processing device), firmware,or a combination thereof. For example, one or more operations of method1000 may be performed by a processing device executing an aligner designanalysis module 1450 of FIG. 14. It should be noted that the method 1000may be performed for each unique aligner for each patient's treatmentplan, or for each unique aligner at key stages of the treatment plan.Further, method 1000 includes operations that may be performed duringblock 104 of FIG. 1A.

The rules engine may use one or more rules that are determined based onobservations, output of numerical simulation, or the like. For example,customers may provide reports that describe an aligner that broke duringremoval, manufacturing technician may observe aligner breakage duringremoval of the aligners from molds, and so forth. Hundreds or thousandsof observations of aligners that broke as a result of force beingapplied may be used to determine patterns or combinations of featuresincluded in the broken aligners that may have caused the breakage. Therules may be determined that specify there is a probable point of damagewhen the patterns or combinations of features are present in subsequentdesigns. Further, the numerical simulation may be executed and identifyprobable points of damage as output. The output from hundreds orthousands of numerical simulations may be aggregated and patterns orcombinations of features may be identified that are associated with theprobable points of damage. The rules may be determined that specifythere is a probable point of damage when the patterns or combinations offeatures are present in subsequent designs.

At block 1002, processing logic may perform the analysis on the digitaldesign of the aligner using a rules engine including one or more rulesassociated with parameters of the aligners indicative of points ofdamage, which may include performing operations at blocks 1004 and 1006.The rules may include rules associated with sets of parameters (e.g.,multiple features within a threshold proximity with one another) and/orwith individual parameters. At block 1004, processing logic maydetermine the parameters of the aligner based on the digital design ofthe polymeric aligner. The parameters may include at least one of anangle of a cutline at locations of the aligner associated with aninterproximal region of the dental arch of the patient, a curvature ofthe aligner, a thickness of the aligner, an undercut height associatedwith an attachment of a tooth of the tooth of the dental arch of thepatient, whether features are present in the aligner, a distance betweenfeatures of the aligner associated with attachments of teeth of thedental arch of the patient, a number of the features of the aligner,and/or a combination of the features of the aligner. Any one or more ofthese parameters may be indicative of a probable point of damage in thedigital design of the aligner as determined from historical patientfeedback, the trained machine learning model, and/or running any of thenumerical simulations described above. The rules may be created based onone or more of the parameters.

At block 1006, for each parameter of the parameters, processing logicmay perform operations at blocks 1008 and 1010. Processing logic mayadditionally perform the operations at blocks 1008 and 1010 based on oneor more combinations of parameters and/or based on all of the identifiedparameters. At block 1008, processing logic may determine whether theone or more rules indicate that the parameter (or set of parameters)satisfies a criterion. The criterion may relate to a threshold valuebeing exceeded by the parameter or a presence of certain featuresindicated by the parameter or parameters. For example, if there is anattachment on a certain tooth and another attachment on a neighboringtooth, the rule may indicate there is a probable point of damage betweenthe two teeth. In another example, if an angle of a cutline is more thana threshold angle, the rule may indicate there is a probable point ofdamage at the location of the cutline. Rules may also be associated withparticular teeth. For example, different threshold angles for thecutline may be associated with interproximal regions between differentpairs of teeth.

Accordingly, at block 1010, processing logic may determine that alocation of the digital design of the aligner associated with theparameter is a probable point of damage responsive to determining thatthe parameter satisfies the criteria of the one or more rules. One ormore corrective actions may be performed in response to determining thatthere is a probable point of damage. In some embodiments, the digitaldesign of the aligner may be input into the trained machine learningmodel to verify the probable point of damage, any of the numericalsimulations described above may be performed on the digital design ofthe aligner, or both.

FIG. 11 illustrates a flow diagram for a method 1100 of outputting afiltered set of possible treatment plans, in accordance with oneembodiment. One or more operations of method 1100 are performed byprocessing logic of a computing device. The processing logic may includehardware (e.g., circuitry, dedicated logic, programmable logic,microcode, etc.), software (e.g., instructions executed by a processingdevice), firmware, or a combination thereof. For example, one or moreoperations of method 1100 may be performed by a processing deviceexecuting an aligner design analysis module 1450 of FIG. 14.

At block 1102, processing logic may determine a set of possibletreatment plans each including a set of digital designs of aligners(e.g., polymeric aligners) at a set of treatment stages. The set ofpossible treatment plans may include treatment plans that aredynamically generated based on an intraoral scan of the mouth of thepatient, provided by a doctor, modified by the doctor (e.g., the doctoradds an attachment to a tooth at a particular stage), and so forth.

At block 1104, for each digital design of the aligner of the set ofdigital designs of the aligners of the set of possible treatment plans,processing logic may perform operations at block 1106 and 1108. At block1106, processing logic may perform the analysis on the digital design ofthe aligner. The analysis may include using at least one of a) thetrained machine learning model, b) any one or more of the numericalsimulations, or c) the rules engine. In some embodiments, the analysismay include using the rules engine to identify a probable point ofdamage and then inputting the digital design of the aligner into thetrained machine learning model and/or running any of the numericalsimulations described above on the digital design of the aligner toverify the probable point of damage. In another embodiment, the digitaldesign of the aligner may be input into the trained machine learningmodel which may output an existence of a probable point of damage in thedigital design of the aligner (and optionally a location of the probablepoint of damage), and the numerical simulation may be performed on thedigital design of the aligner to verify the existence and/or location ofa probable point of damage. In another embodiment, any one or morenumerical simulations described above may be performed on the digitaldesign of the aligner to determine that there is a probable point ofdamage, and the digital design of the aligner may be input into thetrained machine learning model to verify the probable point of damage.

At block 1108, processing logic may determine, based on the analysis,whether the digital design of the aligner includes the one or moreprobable points of damage.

At block 1110, processing logic may filter out treatment plansassociated with digital designs of one or more aligners that haveprobable points of damages from the set of possible treatment plans tocreate a filtered set of possible treatment plans.

At block 1112, processing logic may output at least one possibletreatment plan of the filtered set of possible treatment plans. Thefiltered set of possible treatment plans may lack digital designs ofaligners having probable points of damage. In some embodiments, if theprobable points of damage cannot be resolved, notifications may beprovided to the doctor that one or more of the digital designs of thealigners includes a probable point of damage and recommend the doctorprovide instructions on how to properly remove the aligner to lower thechance of damage, move including an attachment on one tooth to a laterstage in the treatment plan, or the like.

FIG. 12 illustrates a flow diagram for a method 1200 of performingnumerical simulation on digital designs of an aligner (e.g., a polymericaligner) to generate a rules engine, in accordance with one embodiment.One or more operations of method 1200 are performed by processing logicof a computing device. The processing logic may include hardware (e.g.,circuitry, dedicated logic, programmable logic, microcode, etc.),software (e.g., instructions executed by a processing device), firmware,or a combination thereof. For example, one or more operations of method1200 may be performed by a processing device executing an aligner designanalysis module 1450 of FIG. 14.

At block 1202, processing logic may perform the analysis on a set ofdigital designs of the aligner using any of the numerical simulationsdescribed above multiple times to determine a pattern or combination offeatures or parameters of the aligner that are associated with the oneor more probable points of damage. The pattern or combination offeatures or parameters may include attachments being too crowded, teethbeing too crowded, a outline angle exceeding a threshold value, athickness of the aligner being too thin, etc.

At block 1204, processing logic may generate the rules engine using thepattern or the combination of features or parameters to create the oneor more rules obtained from performing the analysis on the set ofdigital designs of the aligner using the numerical simulation multipletimes. In some embodiments, once the rules engine is generated, thedigital designs of the aligners may be processed by the rules engineprior to having any numerical simulations performed or being input intothe trained machine learning model. If the rules engine indicates thereis a probable point of damage included in a digital design of thealigner, further analysis may perform numerical simulation on thedigital design of the aligner and/or inputting the digital design of thealigner into the trained machine learning model.

FIG. 13 illustrates a flow diagram for a method 1300 of using a rulesengine and/or a trained machine learning model on a digital design of analigner (e.g., a polymeric aligner) to identify a probable point ofdamage and then performing a numerical simulation of the digital designof the aligner, in accordance with one embodiment. One or moreoperations of method 1300 are performed by processing logic of acomputing device. The processing logic may include hardware (e.g.,circuitry, dedicated logic, programmable logic, microcode, etc.),software (e.g., instructions executed by a processing device), firmware,or a combination thereof. For example, one or more operations of method1300 may be performed by a processing device executing an aligner designanalysis module 1450 of FIG. 14.

At block 1302, processing logic may perform the analysis on the digitaldesign of the aligner using the rules engine including the one or morerules associated with the parameters of the aligners indicative of thepoints of damage without performing the numerical simulation. The rulesengine may indicate that there is a probable point of damage included inthe digital design of the aligner based on the parameters of the digitaldesign of the aligner.

At block 1303, processing logic may determine whether there are one ormore probable points of damage detected using the rules engine and/orthe trained machine learning model. If there is not one or more probablepoint of damage detected in the aligner, the method 1300 may conclude.If there is one or more probable point of damage detected in thealigner, at block 1304, processing logic may perform the analysis on thedigital design of the aligner using the numerical simulation to confirmthat there are one or more probable points of damage included in thealigner.

At block 1305, processing logic may determine whether there is one ormore probable points confirmed using the numerical simulation. If not,the method 1300 may conclude. If the processing logic confirms there areone or more probable points of damage using the numerical simulation, atblock 1306, processing logic may perform one or more corrective actionsbased on the one or more probable points of damage.

FIG. 14 illustrates a diagrammatic representation of a machine in theexample form of a computing device 1400 within which a set ofinstructions, for causing the machine to perform any one or more of themethodologies discussed herein (e.g., the methods of FIGS. 1-13). Insome embodiments, the machine may be part of a design station orcommunicatively coupled to the design station. In alternativeembodiments, the machine may be connected (e.g., networked) to othermachines in a Local Area Network (LAN), an intranet, an extranet, or theInternet. For example, the machine may be networked to the designstation and/or a rapid prototyping apparatus such as a 3D printer or SLAapparatus. The machine may operate in the capacity of a server or aclient machine in a client-server network environment, or as a peermachine in a peer-to-peer (or distributed) network environment. Themachine may be a personal computer (PC), a tablet computer, a set-topbox (STB), a Personal Digital Assistant (PDA), a cellular telephone, aweb appliance, a server, a network router, switch or bridge, or anymachine capable of executing a set of instructions (sequential orotherwise) that specify actions to be taken by that machine. Further,while only a single machine is illustrated, the term “machine” shallalso be taken to include any collection of machines (e.g., computers)that individually or jointly execute a set (or multiple sets) ofinstructions to perform any one or more of the methodologies discussedherein.

The example computer device 1400 (also referred to as a computingdevice) includes a processing device 1402, a main memory 1404 (e.g.,read-only memory (ROM), flash memory, dynamic random access memory(DRAM) such as synchronous DRAM (SDRAM), etc.), a static memory 1406(e.g., flash memory, static random access memory (SRAM), etc.), and asecondary memory (e.g., a data storage device 1428), which communicatewith each other via a bus 1408.

Processing device 1402 represents one or more general-purpose processorssuch as a microprocessor, central processing unit, or the like. Moreparticularly, the processing device 1402 may be a complex instructionset computing (CISC) microprocessor, reduced instruction set computing(RISC) microprocessor, very long instruction word (VLIW) microprocessor,processor implementing other instruction sets, or processorsimplementing a combination of instruction sets. Processing device 1402may also be one or more special-purpose processing devices such as anapplication specific integrated circuit (ASIC), a field programmablegate array (FPGA), a digital signal processor (DSP), network processor,or the like. Processing device 1402 is configured to execute theprocessing logic (instructions 1426) for performing operations and stepsdiscussed herein.

The computing device 1400 may further include a network interface device1422 for communicating with a network 1464. The computing device 1400also may include a video display unit 1410 (e.g., a liquid crystaldisplay (LCD) or a cathode ray tube (CRT)), an alphanumeric input device1412 (e.g., a keyboard), a cursor control device 1414 (e.g., a mouse),and a signal generation device 1420 (e.g., a speaker).

The data storage device 1428 may include a machine-readable storagemedium (or more specifically a non-transitory computer-readable storagemedium) 1424 on which is stored one or more sets of instructions 1426embodying any one or more of the methodologies or functions describedherein. A non-transitory storage medium refers to a storage medium otherthan a carrier wave. The instructions 1426 may also reside, completelyor at least partially, within the main memory 1404 and/or within theprocessing device 1402 during execution thereof by the computer device1400, the main memory 1404 and the processing device 1402 alsoconstituting computer-readable storage media.

The computer-readable storage medium 1424 may also be used to store oneor more digital models of aligners and/or dental arches (also referredto as electronic models) and/or an aligner design analysis module 1450,which may perform one or more of the operations of the methods describedherein. The computer-readable storage medium 1424 may also store asoftware library containing methods that call an aligner design analysismodule 1450. While the computer-readable storage medium 1424 is shown inan example embodiment to be a single medium, the term “computer-readablestorage medium” should be taken to include a single medium or multiplemedia (e.g., a centralized or distributed database, and/or associatedcaches and servers) that store the one or more sets of instructions. Theterm “computer-readable storage medium” shall also be taken to includeany medium that is capable of storing or encoding a set of instructionsfor execution by the machine and that cause the machine to perform anyone or more of the methodologies of the present disclosure. The term“computer-readable storage medium” shall accordingly be taken toinclude, but not be limited to, solid-state memories, and optical andmagnetic media.

FIG. 15A illustrates an exemplary tooth repositioning appliance oraligner 1500 that can be worn by a patient in order to achieve anincremental repositioning of individual teeth 1502 in the jaw. Theappliance can include a shell (e.g., a continuous polymeric shell or asegmented shell) having teeth-receiving cavities that receive andresiliently reposition the teeth. An appliance or portion(s) thereof maybe indirectly fabricated using a physical model of teeth. For example,an appliance (e.g., polymeric appliance) can be formed using a physicalmodel of teeth and a sheet of suitable layers of polymeric material. A“polymeric material,” as used herein, may include any material formedfrom a polymer. A “polymer,” as used herein, may refer to a moleculecomposed of repeating structural units connected by covalent chemicalbonds often characterized by a substantial number of repeating units(e.g., equal to or greater than 3 repeating units, optionally, in someembodiments equal to or greater than 10 repeating units, in someembodiments greater or equal to 30 repeating units) and a high molecularweight (e.g. greater than or equal to 10,000 Da, in some embodimentsgreater than or equal to 50,000 Da or greater than or equal to 100,000Da). Polymers are commonly the polymerization product of one or moremonomer precursors. The term polymer includes homopolymers, or polymersconsisting essentially of a single repeating monomer subunit. The termpolymer also includes copolymers which are formed when two or moredifferent types of monomers are linked in the same polymer. Usefulpolymers include organic polymers or inorganic polymers that may be inamorphous, semi-amorphous, crystalline or semi-crystalline states.Polymers may include polyolefins, polyesters, polyacrylates,polymethacrylates, polystyrenes, Polypropylenes, polyethylenes,Polyethylene terephthalates, poly lactic acid, polyurethanes, epoxidepolymers, polyethers, poly(vinyl chlorides), polysiloxanes,polycarbonates, polyamides, poly acrylonitriles, polybutadienes,poly(cycloolefins), and copolymers. The systems and/or methods providedherein are compatible with a range of plastics and/or polymers.Accordingly, this list is not all inclusive, but rather is exemplary.The plastics can be thermosets or thermoplastics. The plastic may be athermoplastic.

Examples of materials applicable to the embodiments disclosed hereininclude, but are not limited to, those materials described in thefollowing published and provisional patent applications filed by AlignTechnology: “MULTI-MATERIAL ALIGNERS,” US Publication No. 2017/0007361published Jan. 12, 2017; “DIRECT FABRICATION OF ALIGNERS WITHINTERPROXIMAL FORCE COUPLING”, US Publication No. 2017/0007365 publishedJan. 12, 2017; “DIRECT FABRICATION OF ORTHODONTIC APPLIANCES WITHVARIABLE PROPERTIES,” US Publication No. 2017/0007359 published Jan. 12,2017; “DIRECT FABRICATION OF ALIGNERS FOR ARCH EXPANSION”, USPublication No. 2017/0007366 published Jan. 12, 2017; “DIRECTFABRICATION OF ATTACHMENT TEMPLATES WITH ADHESIVE,” US Publication No.2017/0007368 published Jan. 12, 2017; “DIRECT FABRICATION OF ALIGNERSFOR PALATE EXPANSION AND OTHER APPLICATIONS”, US Publication No.2017/0007367 published Jan. 12, 2017; “SYSTEMS, APPARATUSES AND METHODSFOR DENTAL APPLIANCES WITH INTEGRALLY FORMED FEATURES”, US PublicationNo. 2017/0007360 published Jan. 12, 2017; “DIRECT FABRICATION OF POWERARMS”, US Publication No. 2017/0007363 published Jan. 12, 2017;“SYSTEMS, APPARATUSES AND METHODS FOR SUBSTANCE DELIVERY FROM DENTALAPPLIANCE”, US Publication No. 2017/0007386 published Jan. 12, 2017;“DENTAL APPLIANCE HAVING ORNAMENTAL DESIGN”, US Publication No.2017/0008333 published Jan. 12, 2017; “DENTAL MATERIALS USING THERMOSETPOLYMERS,” US Publication No. 2017/0007362 published Jan. 12, 2017;“CURABLE COMPOSITION FOR USE IN A HIGH TEMPERATURE LITHOGRAPHY-BASEDPHOTOPOLYMERIZATION PROCESS AND METHOD OF PRODUCING CROSSLINKED POLYMERSTHEREFROM,” U.S. Provisional Application Ser. No. 62/667,354, filed May4, 2018; “POLYMERIZABLE MONOMERS AND METHOD OF POLYMERIZING THE SAME,”U.S. Provisional Application Ser. No. 62/667,364, filed May 4, 2018; andany conversion applications thereof (including publications and issuedpatents), including any divisional, continuation, orcontinuation-in-part thereof.

Although polymeric aligners are discussed herein, the techniquesdisclosed may also be applied to aligners having different materials.Some embodiments are discussed herein with reference to orthodonticaligners (also referred to simply as aligners). However, embodimentsalso extend to other types of shells formed over molds, such asorthodontic retainers, orthodontic splints, sleep appliances for mouthinsertion (e.g., for minimizing snoring, sleep apnea, etc.) and/orshells for non-dental applications. Accordingly, it should be understoodthat embodiments herein that refer to aligners also apply to other typesof shells. For example, the principles, features and methods discussedmay be applied to any application or process in which it is useful toperform image based quality control for any suitable type of shells thatare form fitting devices such as eye glass frames, contact or glasslenses, hearing aids or plugs, artificial knee caps, prosthetic limbsand devices, orthopedic inserts, as well as protective equipment such asknee guards, athletic cups, or elbow, chin, and shin guards and otherlike athletic/protective devices.

The aligner 1500 can fit over all teeth present in an upper or lowerjaw, or less than all of the teeth. The appliance can be designedspecifically to accommodate the teeth of the patient (e.g., thetopography of the tooth-receiving cavities matches the topography of thepatient's teeth), and may be fabricated based on positive or negativemodels of the patient's teeth generated by impression, scanning, and thelike. Alternatively, the appliance can be a generic appliance configuredto receive the teeth, but not necessarily shaped to match the topographyof the patient's teeth. In some cases, only certain teeth received by anappliance will be repositioned by the appliance while other teeth canprovide a base or anchor region for holding the appliance in place as itapplies force against the tooth or teeth targeted for repositioning. Insome cases, some, most, or even all of the teeth will be repositioned atsome point during treatment. Teeth that are moved can also serve as abase or anchor for holding the appliance as it is worn by the patient.Typically, no wires or other means will be provided for holding anappliance in place over the teeth. In some cases, however, it may bedesirable or necessary to provide individual attachments or otheranchoring elements 1504 on teeth 1502 with corresponding receptacles orapertures 1506 in the aligner 1500 so that the appliance can apply aselected force on the tooth. Exemplary appliances, including thoseutilized in the Invisalign® System, are described in numerous patentsand patent applications assigned to Align Technology, Inc. including,for example, in U.S. Pat. Nos. 6,450,807, and 5,975,893, as well as onthe company's website, which is accessible on the World Wide Web (see,e.g., the url “invisalign.com”). Examples of tooth-mounted attachmentssuitable for use with orthodontic appliances are also described inpatents and patent applications assigned to Align Technology, Inc.,including, for example, U.S. Pat. Nos. 6,309,215 and 6,830,450.

FIG. 15B illustrates a tooth repositioning system 1510 including aplurality of appliances 1512, 1514, 1516. Any of the appliancesdescribed herein can be designed and/or provided as part of a set of aplurality of appliances used in a tooth repositioning system. Eachappliance may be configured so a tooth-receiving cavity has a geometrycorresponding to an intermediate or final tooth arrangement intended forthe appliance. The patient's teeth can be progressively repositionedfrom an initial tooth arrangement to a target tooth arrangement byplacing a series of incremental position adjustment appliances over thepatient's teeth. For example, the tooth repositioning system 1510 caninclude a first appliance 1512 corresponding to an initial tootharrangement, one or more intermediate appliances 1514 corresponding toone or more intermediate arrangements, and a final appliance 1516corresponding to a target arrangement. A target tooth arrangement can bea planned final tooth arrangement selected for the patient's teeth atthe end of all planned orthodontic treatment. Alternatively, a targetarrangement can be one of some intermediate arrangements for thepatient's teeth during the course of orthodontic treatment, which mayinclude various different treatment scenarios, including, but notlimited to, instances where surgery is recommended, where interproximalreduction (IPR) is appropriate, where a progress check is scheduled,where anchor placement is best, where palatal expansion is desirable,where restorative dentistry is involved (e.g., inlays, onlays, crowns,bridges, implants, veneers, and the like), etc. As such, it isunderstood that a target tooth arrangement can be any planned resultingarrangement for the patient's teeth that follows one or more incrementalrepositioning stages. Likewise, an initial tooth arrangement can be anyinitial arrangement for the patient's teeth that is followed by one ormore incremental repositioning stages.

In some embodiments, the appliances 1512, 1514, 1516 (or portionsthereof) can be produced using indirect fabrication techniques, such asby thermoforming over a positive or negative mold. Indirect fabricationof an orthodontic appliance can involve producing a positive or negativemold of the patient's dentition in a target arrangement (e.g., by rapidprototyping, milling, etc.) and thermoforming one or more sheets ofmaterial over the mold in order to generate an appliance shell.

In an example of indirect fabrication, a mold of a patient's dental archmay be fabricated from a digital model of the dental arch, and a shellmay be formed over the mold (e.g., by thermoforming a polymeric sheetover the mold of the dental arch and then trimming the thermoformedpolymeric sheet). The fabrication of the mold may be performed by arapid prototyping machine (e.g., a stereolithography (SLA) 3D printer).The rapid prototyping machine may receive digital models of molds ofdental arches and/or digital models of the appliances 1512, 1514, 1516after the digital models of the appliances 1512, 1514, 1516 have beenprocessed by processing logic of a computing device, such as thecomputing device in FIG. 14. The processing logic may include hardware(e.g., circuitry, dedicated logic, programmable logic, microcode, etc.),software (e.g., instructions executed by a processing device), firmware,or a combination thereof. For example, one or more operations may beperformed by a processing device executing an appliance design analysisprogram or module 1450.

To manufacture the molds, a shape of a dental arch for a patient at atreatment stage is determined based on a treatment plan. In the exampleof orthodontics, the treatment plan may be generated based on anintraoral scan of a dental arch to be modeled. The intraoral scan of thepatient's dental arch may be performed to generate a three dimensional(3D) virtual model of the patient's dental arch (mold). For example, afull scan of the mandibular and/or maxillary arches of a patient may beperformed to generate 3D virtual models thereof. The intraoral scan maybe performed by creating multiple overlapping intraoral images fromdifferent scanning stations and then stitching together the intraoralimages to provide a composite 3D virtual model. In other applications,virtual 3D models may also be generated based on scans of an object tobe modeled or based on use of computer aided drafting techniques (e.g.,to design the virtual 3D mold). Alternatively, an initial negative moldmay be generated from an actual object to be modeled (e.g., a dentalimpression or the like). The negative mold may then be scanned todetermine a shape of a positive mold that will be produced.

Once the virtual 3D model of the patient's dental arch is generated, adental practitioner may determine a desired treatment outcome, whichincludes final positions and orientations for the patient's teeth.Processing logic may then determine a number of treatment stages tocause the teeth to progress from starting positions and orientations tothe target final positions and orientations. The shape of the finalvirtual 3D model and each intermediate virtual 3D model may bedetermined by computing the progression of tooth movement throughoutorthodontic treatment from initial tooth placement and orientation tofinal corrected tooth placement and orientation. For each treatmentstage, a separate virtual 3D model of the patient's dental arch at thattreatment stage may be generated. The shape of each virtual 3D modelwill be different. The original virtual 3D model, the final virtual 3Dmodel and each intermediate virtual 3D model is unique and customized tothe patient.

Accordingly, multiple different virtual 3D models (digital designs) of adental arch may be generated for a single patient. A first virtual 3Dmodel may be a unique model of a patient's dental arch and/or teeth asthey presently exist, and a final virtual 3D model may be a model of thepatient's dental arch and/or teeth after correction of one or more teethand/or a jaw. Multiple intermediate virtual 3D models may be modeled,each of which may be incrementally different from previous virtual 3Dmodels.

Each virtual 3D model of a patient's dental arch may be used to generatea unique customized physical mold of the dental arch at a particularstage of treatment. The shape of the mold may be at least in part basedon the shape of the virtual 3D model for that treatment stage. Thevirtual 3D model may be represented in a file such as a computer aideddrafting (CAD) file or a 3D printable file such as a stereolithography(STL) file. The virtual 3D model for the mold may be sent to a thirdparty (e.g., clinician office, laboratory, manufacturing facility orother entity). The virtual 3D model may include instructions that willcontrol a fabrication system or device in order to produce the mold withspecified geometries.

A clinician office, laboratory, manufacturing facility or other entitymay receive the virtual 3D model of the mold, the digital model havingbeen created as set forth above. The entity may input the digital modelinto a rapid prototyping machine. The rapid prototyping machine thenmanufactures the mold using the digital model. One example of a rapidprototyping manufacturing machine is a 3D printer. 3D printing includesany layer-based additive manufacturing processes. 3D printing may beachieved using an additive process, where successive layers of materialare formed in proscribed shapes. 3D printing may be performed usingextrusion deposition, granular materials binding, lamination,photopolymerization, continuous liquid interface production (CLIP), orother techniques. 3D printing may also be achieved using a subtractiveprocess, such as milling.

In some instances, stereolithography (SLA), also known as opticalfabrication solid imaging, is used to fabricate an SLA mold. In SLA, themold is fabricated by successively printing thin layers of aphoto-curable material (e.g., a polymeric resin) on top of one another.A platform rests in a bath of a liquid photopolymer or resin just belowa surface of the bath. A light source (e.g., an ultraviolet laser)traces a pattern over the platform, curing the photopolymer where thelight source is directed, to form a first layer of the mold. Theplatform is lowered incrementally, and the light source traces a newpattern over the platform to form another layer of the mold at eachincrement. This process repeats until the mold is completely fabricated.Once all of the layers of the mold are formed, the mold may be cleanedand cured.

Materials such as a polyester, a co-polyester, a polycarbonate, apolycarbonate, a thermopolymeric polyurethane, a polypropylene, apolyethylene, a polypropylene and polyethylene copolymer, an acrylic, acyclic block copolymer, a polyetheretherketone, a polyamide, apolyethylene terephthalate, a polybutylene terephthalate, apolyetherimide, a polyethersulfone, a polytrimethylene terephthalate, astyrenic block copolymer (SBC), a silicone rubber, an elastomeric alloy,a thermopolymeric elastomer (TPE), a thermopolymeric vulcanizate (TPV)elastomer, a polyurethane elastomer, a block copolymer elastomer, apolyolefin blend elastomer, a thermopolymeric co-polyester elastomer, athermopolymeric polyamide elastomer, or combinations thereof, may beused to directly form the mold. The materials used for fabrication ofthe mold can be provided in an uncured form (e.g., as a liquid, resin,powder, etc.) and can be cured (e.g., by photopolymerization, lightcuring, gas curing, laser curing, crosslinking, etc.). The properties ofthe material before curing may differ from the properties of thematerial after curing.

Appliances may be formed from each mold and when applied to the teeth ofthe patient, may provide forces to move the patient's teeth as dictatedby the treatment plan. The shape of each appliance is unique andcustomized for a particular patient and a particular treatment stage. Inan example, the appliances 1512, 1514, 1516 can be pressure formed orthermoformed over the molds. Each mold may be used to fabricate anappliance that will apply forces to the patient's teeth at a particularstage of the orthodontic treatment. The appliances 1512, 1514, 1516 eachhave teeth-receiving cavities that receive and resiliently repositionthe teeth in accordance with a particular treatment stage.

In one embodiment, a sheet of material is pressure formed orthermoformed over the mold. The sheet may be, for example, a sheet ofpolymeric (e.g., an elastic thermopolymeric, a sheet of polymericmaterial, etc.). To thermoform the shell over the mold, the sheet ofmaterial may be heated to a temperature at which the sheet becomespliable. Pressure may concurrently be applied to the sheet to form thenow pliable sheet around the mold. Once the sheet cools, it will have ashape that conforms to the mold. In one embodiment, a release agent(e.g., a non-stick material) is applied to the mold before forming theshell. This may facilitate later removal of the mold from the shell.Forces may be applied to lift the appliance from the mold. In someinstances, a breakage, warpage, or deformation may result from theremoval forces. Accordingly, embodiments disclosed herein may determinewhere the probable point or points of damage may occur in a digitaldesign of the appliance prior to manufacturing and may perform acorrective action.

Additional information may be added to the appliance. The additionalinformation may be any information that pertains to the appliance.Examples of such additional information includes a part numberidentifier, patient name, a patient identifier, a case number, asequence identifier (e.g., indicating which appliance a particular lineris in a treatment sequence), a date of manufacture, a clinician name, alogo and so forth. For example, after determining there is a probablepoint of damage in a digital design of an appliance, an indicator may beinserted into the digital design of the appliance. The indicator mayrepresent a recommended place to begin removing the polymeric applianceto prevent the point of damage from manifesting during removal in someembodiments.

In some embodiments, a library of removal methods/patterns may beestablished and this library may be referenced when simulating theremoval of the aligner in the numerical simulation. Different patientsor production technicians may tend to remove aligners differently, andthere might be a few typical patterns. For example: 1) some patientslift from the lingual side of posteriors first (first left and thenright, or vice versa), and then go around the arch from left/rightposterior section to the right/left posterior section; 2) similar to #1,but some other patients lift only one side of the posterior and then goaround the arch; 3) similar to #1, but some patients lift from thebuccal side rather than the lingual side of the posterior; 4) somepatients lift from the anterior incisors and pull hard to remove thealigner; 5) some other patients grab both lingual and buccal side of aposterior location and pull out both sides at the same time; 6) someother patients grab a random tooth in the middle. The library can alsoinclude a removal guideline provided by the manufacturer of the aligner.Removal approach may also depend on presence or absence of attachmentson teeth as some pf the above method may result in more comfortable wayof removal. Based on the attachment situation on each tooth, it can bedetermined how each patient would probably remove an aligner and adaptthat removal procedure for that patient in that specific simulation.

After an appliance is formed over a mold for a treatment stage, thatappliance is subsequently trimmed along a cutline (also referred to as atrim line) and the appliance may be removed from the mold. Theprocessing logic may determine a cutline for the appliance. Thedetermination of the cutline(s) may be made based on the virtual 3Dmodel of the dental arch at a particular treatment stage, based on avirtual 3D model of the appliance to be formed over the dental arch, ora combination of a virtual 3D model of the dental arch and a virtual 3Dmodel of the appliance. The location and shape of the cutline can beimportant to the functionality of the appliance (e.g., an ability of theappliance to apply desired forces to a patient's teeth) as well as thefit and comfort of the appliance. For shells such as orthodonticappliances, orthodontic retainers and orthodontic splints, the trimmingof the shell may play a role in the efficacy of the shell for itsintended purpose (e.g., aligning, retaining or positioning one or moreteeth of a patient) as well as the fit of the shell on a patient'sdental arch. For example, if too much of the shell is trimmed, then theshell may lose rigidity and an ability of the shell to exert force on apatient's teeth may be compromised. When too much of the shell istrimmed, the shell may become weaker at that location and may be a pointof damage when a patient removes the shell from their teeth or when theshell is removed from the mold. In some embodiments, the cut line may bemodified in the digital design of the appliance as one of the correctiveactions taken when a probable point of damage is determined to exist inthe digital design of the appliance.

On the other hand, if too little of the shell is trimmed, then portionsof the shell may impinge on a patient's gums and cause discomfort,swelling, and/or other dental issues. Additionally, if too little of theshell is trimmed at a location, then the shell may be too rigid at thatlocation. In some embodiments, the cutline may be a straight line acrossthe appliance at the gingival line, below the gingival line, or abovethe gingival line. In some embodiments, the cutline may be a gingivalcutline that represents an interface between an appliance and apatient's gingiva. In such embodiments, the cutline controls a distancebetween an edge of the appliance and a gum line or gingival surface of apatient.

In embodiments virtual fillers may be used to reduce a likelihood of theoccurrence of probable points of damage. When a probably point of damageis identified, a virtual filler may be added to a region associated withthe probable point of damage or an existing virtual filler at thatregion may be enlarged. For example, virtual fillers in interproximalregions may be added or enlarged.

Each patient has a unique dental arch with unique gingiva. Accordingly,the shape and position of the cutline may be unique and customized foreach patient and for each stage of treatment. For instance, the cutlineis customized to follow along the gum line (also referred to as thegingival line). In some embodiments, the cutline may be away from thegum line in some regions and on the gum line in other regions. Forexample, it may be desirable in some instances for the cutline to beaway from the gum line (e.g., not touching the gum) where the shell willtouch a tooth and on the gum line (e.g., touching the gum) in theinterproximal regions between teeth. Accordingly, it is important thatthe shell be trimmed along a predetermined cutline.

In some embodiments, the orthodontic appliances herein (or portionsthereof) can be produced using direct fabrication, such as additivemanufacturing techniques (also referred to herein as “3D printing) orsubtractive manufacturing techniques (e.g., milling). In someembodiments, direct fabrication involves forming an object (e.g., anorthodontic appliance or a portion thereof) without using a physicaltemplate (e.g., mold, mask etc.) to define the object geometry. Additivemanufacturing techniques can be categorized as follows: (1) vatphotopolymerization (e.g., stereolithography), in which an object isconstructed layer by layer from a vat of liquid photopolymer resin; (2)material jetting, in which material is jetted onto a build platformusing either a continuous or drop on demand (DOD) approach; (3) binderjetting, in which alternating layers of a build material (e.g., apowder-based material) and a binding material (e.g., a liquid binder)are deposited by a print head; (4) fused deposition modeling (FDM), inwhich material is drawn though a nozzle, heated, and deposited layer bylayer; (5) powder bed fusion, including but not limited to direct metallaser sintering (DMLS), electron beam melting (EBM), selective heatsintering (SHS), selective laser melting (SLM), and selective lasersintering (SLS); (6) sheet lamination, including but not limited tolaminated object manufacturing (LOM) and ultrasonic additivemanufacturing (UAM); and (7) directed energy deposition, including butnot limited to laser engineering net shaping, directed lightfabrication, direct metal deposition, and 3D laser cladding. Forexample, stereolithography can be used to directly fabricate one or moreof the appliances 1512, 1514, 1516. In some embodiments,stereolithography involves selective polymerization of a photosensitiveresin (e.g., a photopolymer) according to a desired cross-sectionalshape using light (e.g., ultraviolet light). The object geometry can bebuilt up in a layer-by-layer fashion by sequentially polymerizing aplurality of object cross-sections. As another example, the appliances1512, 1514, 1516 can be directly fabricated using selective lasersintering. In some embodiments, selective laser sintering involves usinga laser beam to selectively melt and fuse a layer of powdered materialaccording to a desired cross-sectional shape in order to build up theobject geometry. As yet another example, the appliances 1512, 1514, 1516can be directly fabricated by fused deposition modeling. In someembodiments, fused deposition modeling involves melting and selectivelydepositing a thin filament of thermoplastic polymer in a layer-by-layermanner in order to form an object. In yet another example, materialjetting can be used to directly fabricate the appliances 1512, 1514,1516. In some embodiments, material jetting involves jetting orextruding one or more materials onto a build surface in order to formsuccessive layers of the object geometry.

In some embodiments, the direct fabrication methods provided hereinbuild up the object geometry in a layer-by-layer fashion, withsuccessive layers being formed in discrete build steps. Alternatively orin combination, direct fabrication methods that allow for continuousbuild-up of an object geometry can be used, referred to herein as“continuous direct fabrication.” Various types of continuous directfabrication methods can be used. As an example, in some embodiments, theappliances 1512, 1514, 1516 are fabricated using “continuous liquidinterphase printing,” in which an object is continuously built up from areservoir of photopolymerizable resin by forming a gradient of partiallycured resin between the building surface of the object and apolymerization-inhibited “dead zone.” In some embodiments, asemi-permeable membrane is used to control transport of aphotopolymerization inhibitor (e.g., oxygen) into the dead zone in orderto form the polymerization gradient. Continuous liquid interphaseprinting can achieve fabrication speeds about 25 times to about 100times faster than other direct fabrication methods, and speeds about1000 times faster can be achieved with the incorporation of coolingsystems. Continuous liquid interphase printing is described in U.S.Patent Publication Nos. 2015/0097315, 2015/0097316, and 2015/0102532,the disclosures of each of which are incorporated herein by reference intheir entirety.

As another example, a continuous direct fabrication method can achievecontinuous build-up of an object geometry by continuous movement of thebuild platform (e.g., along the vertical or Z-direction) during theirradiation phase, such that the hardening depth of the irradiatedphotopolymer is controlled by the movement speed. Accordingly,continuous polymerization of material on the build surface can beachieved. Such methods are described in U.S. Pat. No. 7,892,474, thedisclosure of which is incorporated herein by reference in its entirety.

In another example, a continuous direct fabrication method can involveextruding a composite material composed of a curable liquid materialsurrounding a solid strand. The composite material can be extruded alonga continuous three-dimensional path in order to form the object. Suchmethods are described in U.S. Patent Publication No. 2014/0061974, thedisclosure of which is incorporated herein by reference in its entirety.

In yet another example, a continuous direct fabrication method utilizesa “heliolithography” approach in which the liquid photopolymer is curedwith focused radiation while the build platform is continuously rotatedand raised. Accordingly, the object geometry can be continuously builtup along a spiral build path. Such methods are described in U.S. PatentPublication No. 2014/0265034, the disclosure of which is incorporatedherein by reference in its entirety.

The direct fabrication approaches provided herein are compatible with awide variety of materials, including but not limited to one or more ofthe following: a polyester, a co-polyester, a polycarbonate, athermoplastic polyurethane, a polypropylene, a polyethylene, apolypropylene and polyethylene copolymer, an acrylic, a cyclic blockcopolymer, a polyetheretherketone, a polyamide, a polyethyleneterephthalate, a polybutylene terephthalate, a polyetherimide, apolyethersulfone, a polytrimethylene terephthalate, a styrenic blockcopolymer (SBC), a silicone rubber, an elastomeric alloy, athermoplastic elastomer (TPE), a thermoplastic vulcanizate (TPV)elastomer, a polyurethane elastomer, a block copolymer elastomer, apolyolefin blend elastomer, a thermoplastic co-polyester elastomer, athermoplastic polyamide elastomer, a thermoset material, or combinationsthereof. The materials used for direct fabrication can be provided in anuncured form (e.g., as a liquid, resin, powder, etc.) and can be cured(e.g., by photopolymerization, light curing, gas curing, laser curing,crosslinking, etc.) in order to form an orthodontic appliance or aportion thereof. The properties of the material before curing may differfrom the properties of the material after curing. Once cured, thematerials herein can exhibit sufficient strength, stiffness, durability,biocompatibility, etc. for use in an orthodontic appliance. Thepost-curing properties of the materials used can be selected accordingto the desired properties for the corresponding portions of theappliance.

In some embodiments, relatively rigid portions of the orthodonticappliance can be formed via direct fabrication using one or more of thefollowing materials: a polyester, a co-polyester, a polycarbonate, athermoplastic polyurethane, a polypropylene, a polyethylene, apolypropylene and polyethylene copolymer, an acrylic, a cyclic blockcopolymer, a polyetheretherketone, a polyamide, a polyethyleneterephthalate, a polybutylene terephthalate, a polyetherimide, apolyethersulfone, and/or a polytrimethylene terephthalate.

In some embodiments, relatively elastic portions of the orthodonticappliance can be formed via direct fabrication using one or more of thefollowing materials: a styrenic block copolymer (SBC), a siliconerubber, an elastomeric alloy, a thermoplastic elastomer (TPE), athermoplastic vulcanizate (TPV) elastomer, a polyurethane elastomer, ablock copolymer elastomer, a polyolefin blend elastomer, a thermoplasticco-polyester elastomer, and/or a thermoplastic polyamide elastomer.

Machine parameters can include curing parameters. For digital lightprocessing (DLP)-based curing systems, curing parameters can includepower, curing time, and/or grayscale of the full image. For laser-basedcuring systems, curing parameters can include power, speed, beam size,beam shape and/or power distribution of the beam. For printing systems,curing parameters can include material drop size, viscosity, and/orcuring power. These machine parameters can be monitored and adjusted ona regular basis (e.g., some parameters at every 1-x layers and someparameters after each build) as part of the process control on thefabrication machine. Process control can be achieved by including asensor on the machine that measures power and other beam parametersevery layer or every few seconds and automatically adjusts them with afeedback loop. For DLP machines, gray scale can be measured andcalibrated before, during, and/or at the end of each build, and/or atpredetermined time intervals (e.g., every nth build, once per hour, onceper day, once per week, etc.), depending on the stability of the system.In addition, material properties and/or photo-characteristics can beprovided to the fabrication machine, and a machine process controlmodule can use these parameters to adjust machine parameters (e.g.,power, time, gray scale, etc.) to compensate for variability in materialproperties. By implementing process controls for the fabricationmachine, reduced variability in appliance accuracy and residual stresscan be achieved.

Optionally, the direct fabrication methods described herein allow forfabrication of an appliance including multiple materials, referred toherein as “multi-material direct fabrication.” In some embodiments, amulti-material direct fabrication method involves concurrently formingan object from multiple materials in a single manufacturing step. Forinstance, a multi-tip extrusion apparatus can be used to selectivelydispense multiple types of materials from distinct material supplysources in order to fabricate an object from a plurality of differentmaterials. Such methods are described in U.S. Pat. No. 6,749,414, thedisclosure of which is incorporated herein by reference in its entirety.Alternatively or in combination, a multi-material direct fabricationmethod can involve forming an object from multiple materials in aplurality of sequential manufacturing steps. For instance, a firstportion of the object can be formed from a first material in accordancewith any of the direct fabrication methods herein, then a second portionof the object can be formed from a second material in accordance withmethods herein, and so on, until the entirety of the object has beenformed.

Direct fabrication can provide various advantages compared to othermanufacturing approaches. For instance, in contrast to indirectfabrication, direct fabrication permits production of an orthodonticappliance without utilizing any molds or templates for shaping theappliance, thus reducing the number of manufacturing steps involved andimproving the resolution and accuracy of the final appliance geometry.Additionally, direct fabrication permits precise control over thethree-dimensional geometry of the appliance, such as the appliancethickness. Complex structures and/or auxiliary components can be formedintegrally as a single piece with the appliance shell in a singlemanufacturing step, rather than being added to the shell in a separatemanufacturing step. In some embodiments, direct fabrication is used toproduce appliance geometries that would be difficult to create usingalternative manufacturing techniques, such as appliances with very smallor fine features, complex geometric shapes, undercuts, interproximalstructures, shells with variable thicknesses, and/or internal structures(e.g., for improving strength with reduced weight and material usage).For example, in some embodiments, the direct fabrication approachesherein permit fabrication of an orthodontic appliance with feature sizesof less than or equal to about 5 μm, or within a range from about 5 μmto about 50 μm, or within a range from about 20 μm to about 50 μm.

The direct fabrication techniques described herein can be used toproduce appliances with substantially isotropic material properties,e.g., substantially the same or similar strengths along all directions.In some embodiments, the direct fabrication approaches herein permitproduction of an orthodontic appliance with a strength that varies by nomore than about 25%, about 20%, about 15%, about 10%, about 5%, about1%, or about 0.5% along all directions. Additionally, the directfabrication approaches herein can be used to produce orthodonticappliances at a faster speed compared to other manufacturing techniques.In some embodiments, the direct fabrication approaches herein allow forproduction of an orthodontic appliance in a time interval less than orequal to about 1 hour, about 30 minutes, about 25 minutes, about 20minutes, about 15 minutes, about 10 minutes, about 5 minutes, about 4minutes, about 3 minutes, about 2 minutes, about 1 minutes, or about 30seconds. Such manufacturing speeds allow for rapid “chair-side”production of customized appliances, e.g., during a routine appointmentor checkup.

In some embodiments, the direct fabrication methods described hereinimplement process controls for various machine parameters of a directfabrication system or device in order to ensure that the resultantappliances are fabricated with a high degree of precision. Suchprecision can be beneficial for ensuring accurate delivery of a desiredforce system to the teeth in order to effectively elicit toothmovements. Process controls can be implemented to account for processvariability arising from multiple sources, such as the materialproperties, machine parameters, environmental variables, and/orpost-processing parameters.

Material properties may vary depending on the properties of rawmaterials, purity of raw materials, and/or process variables duringmixing of the raw materials. In many embodiments, resins or othermaterials for direct fabrication should be manufactured with tightprocess control to ensure little variability in photo-characteristics,material properties (e.g., viscosity, surface tension), physicalproperties (e.g., modulus, strength, elongation) and/or thermalproperties (e.g., glass transition temperature, heat deflectiontemperature). Process control for a material manufacturing process canbe achieved with screening of raw materials for physical propertiesand/or control of temperature, humidity, and/or other process parametersduring the mixing process. By implementing process controls for thematerial manufacturing procedure, reduced variability of processparameters and more uniform material properties for each batch ofmaterial can be achieved. Residual variability in material propertiescan be compensated with process control on the machine, as discussedfurther herein.

Machine parameters can include curing parameters. For digital lightprocessing (DLP)-based curing systems, curing parameters can includepower, curing time, and/or grayscale of the full image. For laser-basedcuring systems, curing parameters can include power, speed, beam size,beam shape and/or power distribution of the beam. For printing systems,curing parameters can include material drop size, viscosity, and/orcuring power. These machine parameters can be monitored and adjusted ona regular basis (e.g., some parameters at every 1-x layers and someparameters after each build) as part of the process control on thefabrication machine. Process control can be achieved by including asensor on the machine that measures power and other beam parametersevery layer or every few seconds and automatically adjusts them with afeedback loop. For DLP machines, gray scale can be measured andcalibrated at the end of each build. In addition, material propertiesand/or photo-characteristics can be provided to the fabrication machine,and a machine process control module can use these parameters to adjustmachine parameters (e.g., power, time, gray scale, etc.) to compensatefor variability in material properties. By implementing process controlsfor the fabrication machine, reduced variability in appliance accuracyand residual stress can be achieved.

In many embodiments, environmental variables (e.g., temperature,humidity, Sunlight or exposure to other energy/curing source) aremaintained in a tight range to reduce variable in appliance thicknessand/or other properties. Optionally, machine parameters can be adjustedto compensate for environmental variables.

In many embodiments, post-processing of appliances includes cleaning,post-curing, and/or support removal processes. Relevant post-processingparameters can include purity of cleaning agent, cleaning pressureand/or temperature, cleaning time, post-curing energy and/or time,and/or consistency of support removal process. These parameters can bemeasured and adjusted as part of a process control scheme. In addition,appliance physical properties can be varied by modifying thepost-processing parameters. Adjusting post-processing machine parameterscan provide another way to compensate for variability in materialproperties and/or machine properties.

The configuration of the orthodontic appliances herein can be determinedaccording to a treatment plan for a patient, e.g., a treatment planinvolving successive administration of a plurality of appliances forincrementally repositioning teeth. Computer-based treatment planningand/or appliance manufacturing methods can be used in order tofacilitate the design and fabrication of appliances. For instance, oneor more of the appliance components described herein can be digitallydesigned and fabricated with the aid of computer-controlledmanufacturing devices (e.g., computer numerical control (CNC) milling,computer-controlled rapid prototyping such as 3D printing, etc.). Thecomputer-based methods presented herein can improve the accuracy,flexibility, and convenience of appliance fabrication.

FIG. 15C illustrates a method 1550 of orthodontic treatment using aplurality of appliances (e.g., a plurality of aligners), in accordancewith embodiments. The method 1550 can be practiced using any of theappliances or appliance sets described herein. In block 1560, a firstorthodontic appliance is applied to a patient's teeth in order toreposition the teeth from a first tooth arrangement to a second tootharrangement. In block 1570, a second orthodontic appliance is applied tothe patient's teeth in order to reposition the teeth from the secondtooth arrangement to a third tooth arrangement. The method 1550 can berepeated as necessary using any suitable number and combination ofsequential appliances in order to incrementally reposition the patient'steeth from an initial arrangement to a target arrangement. Theappliances can be generated all at the same stage or in sets or batches(e.g., at the beginning of a stage of the treatment), or the appliancescan be fabricated one at a time, and the patient can wear each applianceuntil the pressure of each appliance on the teeth can no longer be feltor until the maximum amount of expressed tooth movement for that givenstage has been achieved. A plurality of different appliances (e.g., aset) can be designed and even fabricated prior to the patient wearingany appliance of the plurality. After wearing an appliance for anappropriate period of time, the patient can replace the currentappliance with the next appliance in the series until no more appliancesremain. The appliances are generally not affixed to the teeth and thepatient may place and replace the appliances at any time during theprocedure (e.g., patient-removable appliances). The final appliance orseveral appliances in the series may have a geometry or geometriesselected to overcorrect the tooth arrangement. For instance, one or moreappliances may have a geometry that would (if fully achieved) moveindividual teeth beyond the tooth arrangement that has been selected asthe “final.” Such over-correction may be desirable in order to offsetpotential relapse after the repositioning method has been terminated(e.g., permit movement of individual teeth back toward theirpre-corrected positions). Over-correction may also be beneficial tospeed the rate of correction (e.g., an appliance with a geometry that ispositioned beyond a desired intermediate or final position may shift theindividual teeth toward the position at a greater rate). In such cases,the use of an appliance can be terminated before the teeth reach thepositions defined by the appliance. Furthermore, over-correction may bedeliberately applied in order to compensate for any inaccuracies orlimitations of the appliance.

FIG. 16 illustrates a method 1600 for designing an orthodontic applianceto be produced by direct fabrication, in accordance with embodiments.The method 1600 can be applied to any embodiment of the orthodonticappliances described herein. Some or all of the blocks of the method1600 can be performed by any suitable data processing system or device,e.g., one or more processors configured with suitable instructions.

In block 1610, a movement path to move one or more teeth from an initialarrangement to a target arrangement is determined. The initialarrangement can be determined from a mold or a scan of the patient'steeth or mouth tissue, e.g., using wax bites, direct contact scanning,x-ray imaging, tomographic imaging, sonographic imaging, and othertechniques for obtaining information about the position and structure ofthe teeth, jaws, gums and other orthodontically relevant tissue. Fromthe obtained data, a digital data set can be derived that represents theinitial (e.g., pretreatment) arrangement of the patient's teeth andother tissues. Optionally, the initial digital data set is processed tosegment the tissue constituents from each other. For example, datastructures that digitally represent individual tooth crowns can beproduced. Advantageously, digital models of entire teeth can beproduced, including measured or extrapolated hidden surfaces and rootstructures, as well as surrounding bone and soft tissue.

The target arrangement of the teeth (e.g., a desired and intended endresult of orthodontic treatment) can be received from a clinician in theform of a prescription, can be calculated from basic orthodonticprinciples, and/or can be extrapolated computationally from a clinicalprescription. With a specification of the desired final positions of theteeth and a digital representation of the teeth themselves, the finalposition and surface geometry of each tooth can be specified to form acomplete model of the tooth arrangement at the desired end of treatment.

Having both an initial position and a target position for each tooth, amovement path can be defined for the motion of each tooth. In someembodiments, the movement paths are configured to move the teeth in thequickest fashion with the least amount of round-tripping to bring theteeth from their initial positions to their desired target positions.The tooth paths can optionally be segmented, and the segments can becalculated so that each tooth's motion within a segment stays withinthreshold limits of linear and rotational translation. In this way, theend points of each path segment can constitute a clinically viablerepositioning, and the aggregate of segment end points can constitute aclinically viable sequence of tooth positions, so that moving from onepoint to the next in the sequence does not result in a collision ofteeth.

In block 1620, a force system to produce movement of the one or moreteeth along the movement path is determined. A force system can includeone or more forces and/or one or more torques. Different force systemscan result in different types of tooth movement, such as tipping,translation, rotation, extrusion, intrusion, root movement, etc.Biomechanical principles, modeling techniques, forcecalculation/measurement techniques, and the like, including knowledgeand approaches commonly used in orthodontia, may be used to determinethe appropriate force system to be applied to the tooth to accomplishthe tooth movement. In determining the force system to be applied,sources may be considered including literature, force systems determinedby experimentation or virtual modeling, computer-based modeling,clinical experience, minimization of unwanted forces, etc.

The determination of the force system can include constraints on theallowable forces, such as allowable directions and magnitudes, as wellas desired motions to be brought about by the applied forces. Forexample, in fabricating palatal expanders, different movement strategiesmay be desired for different patients. For example, the amount of forceneeded to separate the palate can depend on the age of the patient, asvery young patients may not have a fully-formed suture. Thus, injuvenile patients and others without fully-closed palatal sutures,palatal expansion can be accomplished with lower force magnitudes.Slower palatal movement can also aid in growing bone to fill theexpanding suture. For other patients, a more rapid expansion may bedesired, which can be achieved by applying larger forces. Theserequirements can be incorporated as needed to choose the structure andmaterials of appliances; for example, by choosing palatal expanderscapable of applying large forces for rupturing the palatal suture and/orcausing rapid expansion of the palate. Subsequent appliance stages canbe designed to apply different amounts of force, such as first applyinga large force to break the suture, and then applying smaller forces tokeep the suture separated or gradually expand the palate and/or arch.

The determination of the force system can also include modeling of thefacial structure of the patient, such as the skeletal structure of thejaw and palate. Scan data of the palate and arch, such as Xray data or3D optical scanning data, for example, can be used to determineparameters of the skeletal and muscular system of the patient's mouth,so as to determine forces sufficient to provide a desired expansion ofthe palate and/or arch. In some embodiments, the thickness and/ordensity of the mid-palatal suture may be measured, or input by atreating professional. In other embodiments, the treating professionalcan select an appropriate treatment based on physiologicalcharacteristics of the patient. For example, the properties of thepalate may also be estimated based on factors such as the patient'sage—for example, young juvenile patients will typically require lowerforces to expand the suture than older patients, as the suture has notyet fully formed.

In block 1630, an orthodontic appliance configured to produce the forcesystem is determined. Determination of the orthodontic appliance,appliance geometry, material composition, and/or properties can beperformed using a treatment or force application simulation environment.A simulation environment can include, e.g., computer modeling systems,biomechanical systems or apparatus, and the like. Optionally, digitalmodels of the appliance and/or teeth can be produced, such as finiteelement models. The finite element models can be created using computerprogram application software available from a variety of vendors. Forcreating solid geometry models, computer aided engineering (CAE) orcomputer aided design (CAD) programs can be used, such as the AutoCAD®software products available from Autodesk, Inc., of San Rafael, Calif.For creating finite element models and analyzing them, program productsfrom a number of vendors can be used, including finite element analysispackages from ANSYS, Inc., of Canonsburg, Pa., and SIMULIA(Abaqus)software products from Dassault Systémes of Waltham, Mass.

Optionally, one or more orthodontic appliances can be selected fortesting or force modeling. As noted above, a desired tooth movement, aswell as a force system required or desired for eliciting the desiredtooth movement, can be identified. Using the simulation environment, acandidate orthodontic appliance can be analyzed or modeled fordetermination of an actual force system resulting from use of thecandidate appliance. One or more modifications can optionally be made toa candidate appliance, and force modeling can be further analyzed asdescribed, e.g., in order to iteratively determine an appliance designthat produces the desired force system.

In block 1640, instructions for fabrication of the orthodontic applianceincorporating the orthodontic appliance are generated. The instructionscan be configured to control a fabrication system or device in order toproduce the orthodontic appliance with the specified orthodonticappliance. In some embodiments, the instructions are configured formanufacturing the orthodontic appliance using direct fabrication (e.g.,stereolithography, selective laser sintering, fused deposition modeling,3D printing, continuous direct fabrication, multi-material directfabrication, etc.), in accordance with the various methods presentedherein. In alternative embodiments, the instructions can be configuredfor indirect fabrication of the appliance, e.g., by thermoforming.

Method 1600 may comprise additional blocks: 1) The upper arch and palateof the patient is scanned intraorally to generate three dimensional dataof the palate and upper arch; 2) The three dimensional shape profile ofthe appliance is determined to provide a gap and teeth engagementstructures as described herein.

Although the above blocks show a method 1600 of designing an orthodonticappliance in accordance with some embodiments, a person of ordinaryskill in the art will recognize some variations based on the teachingdescribed herein. Some of the blocks may comprise sub-blocks. Some ofthe blocks may be repeated as often as desired. One or more blocks ofthe method 1600 may be performed with any suitable fabrication system ordevice, such as the embodiments described herein. Some of the blocks maybe optional, and the order of the blocks can be varied as desired.

FIG. 17 illustrates a method 1700 for digitally planning an orthodontictreatment and/or design or fabrication of an appliance, in accordancewith embodiments. The method 1700 can be applied to any of the treatmentprocedures described herein and can be performed by any suitable dataprocessing system.

In block 1710, a digital representation of a patient's dental arch isreceived. The digital representation can include surface topography datafor the patient's intraoral cavity (including teeth, gingival tissues,etc.). The surface topography data can be generated by directly scanningthe intraoral cavity, a physical model (positive or negative) of theintraoral cavity, or an impression of the intraoral cavity, using asuitable scanning device (e.g., a handheld scanner, desktop scanner,etc.).

In block 1720, one or more treatment stages are generated based on thedigital representation of the dental arch. The treatment stages can beincremental repositioning stages of an orthodontic treatment proceduredesigned to move one or more of the patient's teeth from an initialtooth arrangement to a target arrangement. For example, the treatmentstages can be generated by determining the initial tooth arrangementindicated by the digital representation, determining a target tootharrangement, and determining movement paths of one or more teeth in theinitial arrangement necessary to achieve the target tooth arrangement.The movement path can be optimized based on minimizing the totaldistance moved, preventing collisions between teeth, avoiding toothmovements that are more difficult to achieve, or any other suitablecriteria.

In block 1730, at least one orthodontic appliance (e.g., at least onealigner) is fabricated based on the generated treatment stages. Forexample, a set of appliances can be fabricated, each shaped according atooth arrangement specified by one of the treatment stages, such thatthe appliances can be sequentially worn by the patient to incrementallyreposition the teeth from the initial arrangement to the targetarrangement. The appliance set may include one or more of theorthodontic appliances described herein. The fabrication of theappliance may involve creating a digital model of the appliance to beused as input to a computer-controlled fabrication system. The appliancecan be formed using direct fabrication methods, indirect fabricationmethods, or combinations thereof, as desired.

In some instances, staging of various arrangements or treatment stagesmay not be necessary for design and/or fabrication of an appliance. Asillustrated by the dashed line in FIG. 17, design and/or fabrication ofan orthodontic appliance, and perhaps a particular orthodontictreatment, may include use of a representation of the patient's teeth(e.g., receive a digital representation of the patient's teeth at block1710), followed by design and/or fabrication of an orthodontic appliancebased on a representation of the patient's teeth in the arrangementrepresented by the received representation.

FIG. 18 illustrates a method 1800 for implementing one or morecorrective actions to a polymeric aligner based on a simulated removalof the polymeric aligner from a dental arch. The method 1800 can beapplied to any of the procedures described herein and can be performedby any suitable data processing system, including the system of FIG. 14.

At block 1802, a first digital model representing a dental arch-likestructure of a patient may be gathered. The dental arch-like structuremay include one or more teeth-like structures of a patient thatinterface with a polymeric aligner. A “dental arch-like structure,” asused herein, may include a structure that has structures that correspondto a dentition of a patient. In some implementations, a dental arch-likestructure comprises a physical mold used to form polymeric aligners. Adental arch-like structure may include regions for attachments, bubbles,and/or other structures adhered (e.g., bonded) to teeth and/ortooth-like structures; and/or pressure areas, power ridges and/or otherstructures subtracted/taken away from teeth and/or teeth-likestructures. A dental arch-like structure may, in variousimplementations, comprise the actual dentition of the patient. A dentalarch-like structure may be identified using physical impressions, scans,and/or techniques used to form a physical mold to indirectly fabricatepolymeric aligners. As a result, in some implementations, the firstdigital model represents a physical mold (prophetic, actual, etc.) thatis used as the basis of indirectly fabricating an aligner. The firstdigital model may include a 3D representation of a physical mold and/ormay correspond to a file (e.g., an STL file) used to fabricate (e.g., 3Dprint) a physical mold of the aligner. The first digital model mayspecify one or more material properties of a physical mold, such as oneor more surface properties of the materials of a physical mold thatwould cause friction against an aligner coupled to that physical mold.In various implementations, the first model of the dental arch-likestructure may comprise may specify one or more physical properties, suchas biomechanical resistance, friction, other surface properties etc.associated with a patient's dentition and/or the patient's wearing of apolymeric aligner on his or her dental arch.

At block 1804, a second digital model representing the polymeric alignerto be supported by the dental arch-like structure may be gathered. Thesecond digital model may include a 3D representation of the polymericaligner and/or may include data related to force(s), torque(s), and/orother orthodontic repositioning elements to be implemented on the dentalarch. In some implementations, the polymeric aligner may include one ormore tooth-receiving cavities configured to apply the repositioningforces to the one or more teeth-like structures of the dental arch-likestructure. The second digital model may specify at least some physicalproperties of the polymeric aligner at one or more regions of thepolymeric aligner. As noted herein, the physical properties maycorrespond to material properties of the polymeric aligner, such asacceptable material strains at various areas. The second digital modelmay specify, for various regions, whether the polymeric aligner islikely to suffer physical damage (e.g., to deform, warp, fail, and/orbreak). In some implementations, the second digital model may break thealigner down into finite elements and may associate the physicalproperties with those finite elements. As noted herein, one or more ofthe finite elements may be characterized by a particular materialproperty that is associated with a particular material strain.

At block 1806, an interaction of the polymeric aligner to the dentalarch-like structure is simulated using the first digital model and thesecond digital model. An example of such an interaction is a coupling,but it is noted the polymeric aligner and the dental arch-like structuremay physically interact with one another without being coupled to oneanother. One or more spatial points of the first digital model may bealigned with corresponding spatial points of the second digital model tosimulate placing the polymeric aligner to the dental arch-likestructure. In some implementations, a virtual spring force may be usedto model interactions between the cavities of the polymeric aligner andcorresponding teeth-like structures in the dental arch-like structure.In various implementations, the interaction may be modeled by alignmentof finite elements of the second digital model against correspondingspatial elements of the first digital model.

At block 1808, removal of the polymeric aligner from the dentalarch-like structure may be simulated using the first digital model andthe second digital model. In some implementations, an interactionbetween the physical properties of the aligner and the second physicalproperties of a physical mold may be simulated. As an example, aninteraction between material properties of the aligner and materialproperties of a physical mold at various regions in space may besimulated. In various implementations, an interaction between physicalproperties of the aligner and physical properties associated withwearing the aligner on the dental arch by a patient (e.g., propertiesassociated with biomechanical forces exerted by teeth and/or propertiesassociated with an intraoral environment) may be simulated.Additionally, simulating removal of the polymeric aligner from thedental arch-like structure may comprise simulating a spring removalforce between cavities of the polymeric aligner and correspondingteeth-like structures. Spring removal forces, as noted herein, maycorrespond to the force sufficient to exceed a virtual spring force(e.g., a modeled force against the polymeric aligner by a mold or dentalarch). Simulating the removal of the polymeric aligner from the dentalarch-like structure may comprise simulating a sequential removal of thepolymeric aligner from a first posterior tooth-like structure of thedental arch-like structure to a second opposing posterior tooth-likestructure of the dental arch-like structure. It is noted simulating theremoval of the polymeric aligner from the dental arch-like structure maycomprise: simulating removal from anterior tooth-like structuresfollowed by posterior tooth-like structures, simulating removal fromattachment-like structures on the dental arch-like structure followed byother structures, etc.

At block 1810, a likeliness of one or more physical strains at the oneor more regions will satisfy one or more strain/stress or deformationenergy-based damage criteria may be determined based on an interactionof the dental arch-like structure and the first one or more physicalproperties, where the interaction is due to the simulated removal.“Strain/stress or deformation energy-based damage criteria,” as usedherein, may include a set of criteria for determining whetherstrains/stresses to a region of a structure will meet, exceed, etc. aspecified threshold. Strain/stress or deformation energy-based criteriamay include numerical scores (e.g., Boolean and/or decimal values) ormay be implemented using various techniques. One or more valuesrepresenting the interaction between the physical properties of thealigner and the physical properties of the or dental arch-like structuremay be determined. These values may represent likeliness of physicalstrains (structural strains, material strains, etc.) on various regionsof the aligner due to removal. As noted herein, each region (e.g., eachfinite element) may have values associated with it. Block 1810 mayinvolve reducing a thickness of the polymeric aligner represented in thesecond digital model until the first one or more physical properties ofthe polymeric aligner at one or more regions of the polymeric alignermeet, exceed, etc. strain/stress or deformation energy-based damagecriteria for the one or more regions.

At block 1812, the second digital model is analyzed for one or morelikely points of structural damage based on the likeliness of the one ormore physical strains at the one or more regions. In someimplementations, values for the physical strains at various regions arecompared to various thresholds (e.g., strain thresholds) for thoseregions. Regions having values below/meeting/exceeding those thresholdsmay be identified.

At block 1814, in response to analyzing the second digital model for theone or more likely points of structural damage, it may be determinedwhether to implement one or more corrective actions for the polymericaligner. In some implementations, the one or more corrective actionscomprise modifying an aligner geometry of the polymeric aligner toaccommodate the one or more likely points of structural damage. Asvarious examples, the one or more corrective actions may guide placementof cut lines, bite ramps, power ridges, attachments, etc. at locationsother than those locations specified in the second digital model. Thecorrective actions may guide modification of aligner thickness ordensity for various regions of the aligner. The corrective actions mayinclude, e.g., instructions to modify fabrication of the aligner asnoted herein and/or instructions to modify a treatment plan, as notedfurther herein.

At block 1816, a third digital model representing the polymeric alignermay be generated. The third digital model may be based on the seconddigital model and the one or more corrective actions for the polymericaligner. The third digital model may represent a modified aligner with,e.g., a modified aligner geometry (modified cut lines, bite ramps, powerridges, attachments, aligner thickness for various regions, etc.). Themodified aligner may be used as the basis of a modified fabricationprocess and/or a modified treatment plan.

In some implementations, fabrication instructions to fabricate amodified polymeric aligner based on the third digital model may beprovided. In some implementations, the fabrication instructions mayinclude: mold formation instructions to form a physical aligner mold forthe polymeric aligner using the third digital model; and/orthermoforming instructions to thermoform the polymeric aligner from asheet of polymeric material placed over the physical aligner mold. Asnoted herein, the third digital model may include one or more structuralfeatures at points relative to corresponding points of the seconddigital model, the one or more structural features being configured toaccommodate the one or more corrective actions. In variousimplementations, the fabrication instructions comprise directfabrication instructions to directly fabricate the polymeric alignerusing the third digital model. As noted herein, the third digital modelmay include one or more areas of modified thickness relative tocorresponding areas of the second digital model, the one or more areasof modified thickness being configured to accommodate the one or morecorrective actions

It is to be understood that the above description is intended to beillustrative, and not restrictive. Many other embodiments will beapparent upon reading and understanding the above description. Althoughembodiments of the present disclosure have been described with referenceto specific example embodiments, it will be recognized that thedisclosure is not limited to the embodiments described, but can bepracticed with modification and alteration within the spirit and scopeof the appended claims. Accordingly, the specification and drawings areto be regarded in an illustrative sense rather than a restrictive sense.The scope of the disclosure should, therefore, be determined withreference to the appended claims, along with the full scope ofequivalents to which such claims are entitled.

1. A method comprising: gathering a first digital model representing adental arch-like structure of a patient, wherein the dental arch-likestructure comprises one or more tooth-like structures to interface witha polymeric aligner; gathering a second digital model representing thepolymeric aligner to be supported by the dental arch-like structure,wherein the polymeric aligner comprises one or more tooth-receivingcavities to receive the one or more tooth-like structures of the dentalarch-like structure, and wherein the second digital model specifiesfirst one or more physical properties of the polymeric aligner at one ormore regions of the polymeric aligner; simulating an interaction of thepolymeric aligner to the dental arch-like structure using the firstdigital model and the second digital model; simulating a removal of thepolymeric aligner from the dental arch-like structure using the firstdigital model and the second digital model to obtain a simulated removalof the polymeric aligner from the dental arch-like structure;determining a likeliness that one or more values at the one or moreregions will satisfy one or more damage criteria, the determinationbeing based on an interaction of the dental arch-like structure and thefirst one or more physical properties of the polymeric aligner, and theinteraction being due to the simulated removal; analyzing the seconddigital model for one or more likely points of physical damage based onthe determination of the likeliness of the one or more values satisfyingthe one or more damage criteria; and in response to analyzing the seconddigital model for the one or more likely points of physical damage,determining whether to implement one or more corrective actions for thepolymeric aligner.
 2. The method of claim 1, wherein the first one ormore physical properties comprise first one or more material propertiesof the polymeric aligner.
 3. The method of claim 1, wherein the one ormore values comprise one or more material strains, stresses, or strainenergies of the polymeric aligner.
 4. The method of claim 1, furthercomprising generating a third digital model representing the polymericaligner, the third digital model being based on the second digital modeland the one or more corrective actions for the polymeric aligner.
 5. Themethod of claim 4, further comprising providing fabrication instructionsto fabricate the polymeric aligner based on the third digital modelcorresponding to the polymeric aligner.
 6. The method of claim 5,wherein the fabrication instructions comprise: mold formationinstructions to form a physical aligner mold for the polymeric alignerusing the third digital model; and thermoforming instructions tothermoform the polymeric aligner from a sheet of polymeric materialplaced over the physical aligner mold.
 7. The method of claim 4, whereinthe third digital model comprises one or more structural features atpoints relative to corresponding points of the second digital model, theone or more structural features being configured to accommodate the oneor more corrective actions.
 8. The method of claim 5, wherein thefabrication instructions comprise direct fabrication instructions todirectly fabricate the polymeric aligner using the third digital model.9. The method of claim 5, wherein: the third digital model comprises oneor more areas of modified thickness relative to corresponding areas ofthe second digital model, the one or more areas of modified thicknessbeing configured to accommodate the one or more corrective actions; andthe fabrication instructions comprise direct fabrication instructions todirectly fabricate the polymeric aligner using the third digital model.10. The method of claim 1, wherein: the dental arch-like structurecomprises a physical mold used to form the polymeric aligner; the firstdigital model specifies second one or more physical properties of thephysical mold; and simulating the removal of the polymeric aligner fromthe dental arch-like structure comprises simulating an interactionbetween the first one or more physical properties of the polymericaligner and the second one or more physical properties of the physicalmold.
 11. The method of claim 1, wherein: the dental arch-like structurecomprises a dental arch of the patient; the first digital modelspecifies third one or more physical properties of the dental arch, thethird one or more physical properties being associated with wearing thepolymeric aligner on the dental arch; and simulating the removal of thepolymeric aligner from the dental arch-like structure comprisessimulating an interaction between the first one or more physicalproperties of the polymeric aligner and the third one or more physicalproperties associated with wearing the polymeric aligner on the dentalarch.
 12. The method of claim 1, wherein simulating the interaction ofthe polymeric aligner to the dental arch-like structure comprisessimulating a virtual spring force between each cavity of the polymericaligner and a corresponding tooth-like structure of the one or moretooth-like structures in the dental arch-like structure.
 13. The methodof claim 12, wherein simulating the removal of the polymeric alignerfrom the dental arch-like structure comprises simulating a springremoval force between each cavity and the corresponding tooth-likestructure, the spring removal force having a magnitude sufficient toexceed the virtual spring force.
 14. The method of claim 13, whereinsimulating the removal of the polymeric aligner from the dentalarch-like structure comprises simulating a sequential removal of thepolymeric aligner from a first posterior tooth-like structure of thedental arch-like structure to a second opposing posterior tooth-likestructure of the dental arch-like structure.
 15. The method of claim 1,wherein the one or more regions of the polymeric aligner correspond tofinite elements of the second digital model, each of the finite elementsbeing characterized by a particular material property associated with atleast one of a particular material strain or a particular stress. 16.The method of claim 1, wherein determining the likeliness that the oneor more values at the one or more regions will satisfy the one or moredamage criteria comprises iteratively modifying a thickness distributionof the polymeric aligner represented in at least one of the seconddigital model, other geometric parameters or treatment planning untilthe one or more values of the polymeric aligner at one or more regionsof the polymeric aligner stop failing the damage criteria for the one ormore regions.
 17. The method of claim 16, wherein the first one or morephysical properties comprise first one or more material properties ofthe polymeric aligner.
 18. The method of claim 16, wherein the one ormore values are not distributed uniformly throughout the polymericaligner.
 19. The method of claim 1, wherein the one or more correctiveactions comprise modifying an aligner geometry of the polymeric alignerto accommodate the one or more likely points of physical damage.
 20. Themethod of claim 19, further comprising providing instructions to modifya treatment plan for a dental arch based on the one or more correctiveactions. 21-41. (canceled)